Unter dem Sofa liegt noch eine Murmel von gestern.

Because unter dem Sofa describes a location: the marble is under the sofa, not moving there.

With two-way prepositions like unter, German uses:

• dative for location
• accusative for direction/movement toward a place

So:

• unter dem Sofa = under the sofa (already there)
• unter das Sofa = to under the sofa / underneath the sofa (moving there)

Here the marble is simply lying there, so dative is required: dem Sofa.

This is because German follows the verb-second rule in main clauses.

The first position can be taken by many different elements, not just the subject. Here, Unter dem Sofa is placed first to emphasize the location. Once that happens, the finite verb must still stay in second position, so it comes next:

• Unter dem Sofa = position 1
• liegt = position 2
• noch eine Murmel von gestern = the rest of the sentence

A more basic order would be:

Eine Murmel von gestern liegt noch unter dem Sofa.

Both are grammatical, but the original sentence puts more focus on where the marble is.

German often uses specific position verbs where English might just use is.

liegen means to lie or to be lying and is commonly used for things that are resting horizontally or simply located somewhere.

So:

• Die Murmel liegt unter dem Sofa. = The marble is lying under the sofa.
• In natural English, you might just say The marble is under the sofa, but German often prefers liegt.

This makes the sentence sound more natural and precise in German.

Here noch means something like still.

So the idea is:

• There is still a marble under the sofa
• or There’s another marble still under the sofa

It suggests that the marble remains there, possibly unexpectedly, or that it has not been removed yet.

In this sentence, noch adds the feeling of persistence: the marble is still there.

Von gestern literally means from yesterday.

In this sentence, it most naturally means that the marble is left over from yesterday or is somehow connected with yesterday. For example, maybe someone was playing yesterday, and one marble is still under the sofa.

So it is not mainly about ownership; it is more about time association:

• eine Murmel von gestern = a marble from yesterday / one left over from yesterday

Grammatically, it most directly attaches to eine Murmel:

eine Murmel von gestern

So the phrase is understood as a marble from yesterday.

But in real meaning, that often blends into the whole situation: there is still a marble under the sofa from yesterday.

So structurally it belongs to Murmel, but semantically it can feel like it comments on the broader situation too.

Murmel is a feminine noun: die Murmel.

In this sentence, eine Murmel is the subject, so it is in the nominative case.

For a feminine noun, the nominative indefinite article is eine:

• die Murmel = the marble
• eine Murmel = a marble

So eine Murmel is correct because it is feminine nominative singular.

Yes. Unter is a two-way preposition.

It takes:

• dative for location
• accusative for movement toward a destination

Compare:

• Die Murmel liegt unter dem Sofa.
  The marble is under the sofa.
  → dative, because it is already there

• Die Murmel rollt unter das Sofa.
  The marble rolls under the sofa.
  → accusative, because it moves to that place

This is a very important pattern in German.

Yes, it is natural.

The original sentence sounds especially natural if the speaker wants to emphasize the location first:

Unter dem Sofa liegt noch eine Murmel von gestern.

A more neutral version could be:

Eine Murmel von gestern liegt noch unter dem Sofa.

Both work, but they highlight different things:

• Unter dem Sofa... = focus on where
• Eine Murmel... = focus on what

German is flexible in this way, as long as the verb-second rule is respected.

Sometimes noch can suggest another/additional, but in this sentence still is the strongest and most natural interpretation.

So the main idea is:

• There is still a marble under the sofa from yesterday.

If you really wanted to emphasize another marble, German would often make that clearer in other ways, depending on context.

So while context can sometimes give noch an additional flavor, here still is the safest understanding.