Atlas › Modular forms › Weight 8 › Level 4 › 4.8.a

Newspace 4.8.a: $S_{8}^{\mathrm{new}}(\Gamma_0(4))$

Newforms

There are no newforms: $S_{8}^{\mathrm{new}}(\Gamma_0(4)) = 0$ .

Dimensions

Newforms $S_{8}^{\mathrm{new}}(\Gamma_0(4))$	0
Old forms	2
Cusp forms $S_{8}(\Gamma_0(4))$	2
Eisenstein series $E_{8}(\Gamma_0(4))$	3
Modular forms $M_{8}(\Gamma_0(4))$	5

Decomposition of the old subspace

$S_{8}^{\mathrm{old}}(\Gamma_0(4)) =$ $S_{8}^{\mathrm{new}}(\Gamma_0(2))^{\oplus 2}$

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(4, 8)

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

cargo run --release -p sagebrush-web --example atlas -- 4:8 1000

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