Atlas › Modular forms › Weight 2 › Level 60 › 60.2.a

Newspace 60.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(60))$

Newforms

There are no newforms: $S_{2}^{\mathrm{new}}(\Gamma_0(60)) = 0$ .

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(60))$	0
Old forms	7
Cusp forms $S_{2}(\Gamma_0(60))$	7
Eisenstein series $E_{2}(\Gamma_0(60))$	11
Modular forms $M_{2}(\Gamma_0(60))$	18

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(60)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(15))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(20))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(30))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0 s (one thread) and proven: the dimensions are certified, and the characteristic polynomial of $T$ over $\mathbb{Z}$ is reconstructed by CRT past a rigorous coefficient bound.

The engine's checks

Open in the notebook · JSON · stored data

Recompute it yourself

In Sage mode at sagebrush.space (or npx sagebrush --sage):

newform_orbits(60, 2)

With the Rust engine (source), in engine/:

cargo run --release -p sagebrush-web --example atlas -- 60:2 1000

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