๐ŸŒฟ Sagebrush Atlas
Atlas โ€บ Modular forms โ€บ Weight 2 โ€บ Level 8 โ€บ 8.2.a

Newspace 8.2.a: S2new(ฮ“0(8))S_{2}^{\mathrm{new}}(\Gamma_0(8))

Newforms

There are no newforms: S2new(ฮ“0(8))=0S_{2}^{\mathrm{new}}(\Gamma_0(8)) = 0.

Dimensions

Newforms S2new(ฮ“0(8))S_{2}^{\mathrm{new}}(\Gamma_0(8))0
Old forms0
Cusp forms S2(ฮ“0(8))S_{2}(\Gamma_0(8))0
Eisenstein series E2(ฮ“0(8))E_{2}(\Gamma_0(8))3
Modular forms M2(ฮ“0(8))M_{2}(\Gamma_0(8))3

Decomposition of the old subspace

The old subspace is 0.

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 TT over Z\mathbb{Z} is reconstructed by CRT past a rigorous coefficient bound.

The engine's checks
    Open in the notebook ยท JSON ยท stored data
    Recompute it yourself

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

    newform_orbits(8, 2)

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

    cargo run --release -p sagebrush-web --example atlas -- 8:2 1000

    โ† 7.2.a ยท 9.2.a โ†’