Mater dicit modestiam etiam in convivio servandam esse.

Because this sentence uses indirect statement after dicit (says). In Latin, indirect statement is usually built with:

• an accusative subject
• plus an infinitive

So modestiam ... servandam esse means literally something like that modesty must be preserved. In that construction, modestiam is the subject of the infinitive phrase, so it goes into the accusative.

This is a passive periphrastic infinitive.

It is made from:

• a gerundive: servandam
• plus esse

The gerundive often expresses necessity or obligation. So servandam esse means:

• to have to be preserved
• must be preserved
• is to be preserved

In this sentence, modestiam servandam esse means that modesty must be preserved.

Because servandam agrees with modestiam.

Modestia is:

• feminine
• singular
• accusative here

So the gerundive must match it:

• feminine
• singular
• accusative

That gives servandam.

This agreement is exactly like an adjective agreeing with a noun.

Because Latin can express must through the gerundive + esse construction.

So instead of using a separate word meaning must, Latin says:

• servanda est = must be preserved
• servandam esse = to have to be preserved / must be preserved in indirect statement

So the idea of obligation is built into servandam itself.

Because servandam is not a complete verb by itself. It is a gerundive, a verbal adjective. To make the full verbal idea, Latin adds esse.

So:

• servandam = needing to be preserved
• servandam esse = to need to be preserved / must be preserved

Since the whole clause depends on dicit, Latin uses the infinitive esse.

Not directly. It may look that way at first, but really modestiam is the subject of the infinitive clause.

The structure is:

• Mater dicit = Mother says
• modestiam etiam in convivio servandam esse = that modesty must be preserved even at a banquet

So dicit does not mean Mother says modesty. It means Mother says that modesty must be preserved...

Etiam means also, even, or sometimes still, depending on context.

Here it goes with in convivio, so the sense is:

• even at a banquet
• even in social dining
• also at a banquet

The most natural understanding is probably even at a banquet, since that highlights a place where modesty might be especially important or especially tested.

Because in with the ablative usually means in or at a place.

So:

• in convivio = at a banquet / in a banquet setting

By contrast, in with the accusative often shows motion into something:

• in convivium = into the banquet

Here there is no motion, only location or setting, so Latin uses the ablative: convivio.

Convivium means a banquet, dinner party, or feast. It often refers not just to the meal itself, but to the social occasion around it.

So in convivio can mean:

• at a banquet
• at a dinner party
• in a social dining setting

Latin word order is much freer than English word order because Latin relies heavily on endings to show grammatical relationships.

So in:

Mater dicit modestiam etiam in convivio servandam esse

you can identify the parts by form:

• Mater = subject of dicit
• dicit = main verb
• modestiam = accusative subject of the infinitive clause
• servandam esse = infinitive phrase expressing obligation
• in convivio = prepositional phrase
• etiam = even / also

Latin often places the infinitive esse at the end, and it often puts important words in emphatic positions. The sentence is not random; it is just less rigid than English.

Not in the same way.

After verbs of saying, thinking, knowing, and perceiving, Latin normally uses accusative + infinitive for indirect statement. So after dicit, the standard construction is exactly what we see here:

• modestiam ... servandam esse

A ut clause is more common after verbs of ordering, persuading, happening, or result expressions, not for ordinary indirect statement after say.

The sentence does not explicitly say who must preserve it. That is normal in this kind of passive obligation construction.

Modestiam servandam esse literally means that modesty must be preserved, without naming the person responsible.

Sometimes Latin adds a dative of agent with this construction if it wants to say who has the duty. For example, something like nobis modestia servanda est would mean we must preserve modesty.

Here the agent is left general or understood from context.

Because Latin has no articles at all. There is no direct equivalent of the or a/an.

So mater could mean:

• mother
• the mother
• a mother

Context decides which is best in translation. In this sentence, Mother says... or The mother says... are both possible depending on context.

Yes. Latin modestia can mean:

• modesty
• self-restraint
• moderation
• proper behavior

So depending on context, the idea may be broader than English modesty in the narrow modern sense. In a sentence about behavior at a banquet, it may suggest decorum or self-control as well.

A very literal breakdown would be:

• Mater = Mother
• dicit = says
• modestiam = modesty
• etiam = even / also
• in convivio = at a banquet
• servandam esse = to have to be preserved

So, very literally:

Mother says modesty even at a banquet to have to be preserved.

That is not good English, of course, but it shows how the Latin grammar works. A more natural English version is:

Mother says that modesty must be preserved even at a banquet.