๐ŸŒฟ Sagebrush Atlas
Atlas โ€บ Modular forms โ€บ Weight 12 โ€บ Level 2 โ€บ 2.12.a

Newspace 2.12.a: S12new(ฮ“0(2))S_{12}^{\mathrm{new}}(\Gamma_0(2))

Newforms

There are no newforms: S12new(ฮ“0(2))=0S_{12}^{\mathrm{new}}(\Gamma_0(2)) = 0.

Dimensions

Newforms S12new(ฮ“0(2))S_{12}^{\mathrm{new}}(\Gamma_0(2))0
Old forms2
Cusp forms S12(ฮ“0(2))S_{12}(\Gamma_0(2))2
Eisenstein series E12(ฮ“0(2))E_{12}(\Gamma_0(2))2
Modular forms M12(ฮ“0(2))M_{12}(\Gamma_0(2))4

Decomposition of the old subspace

S12old(ฮ“0(2))=S_{12}^{\mathrm{old}}(\Gamma_0(2)) = S12new(ฮ“0(1))โŠ•2S_{12}^{\mathrm{new}}(\Gamma_0(1))^{\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 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(2, 12)

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

    cargo run --release -p sagebrush-web --example atlas -- 2:12 1000

    โ† 1.12.a ยท 3.12.a โ†’