Atlas › Modular forms › Weight 12 › Level 23 › 23.12.a

Newspace 23.12.a: $S_{12}^{\mathrm{new}}(\Gamma_0(23))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
23.12.a.a	8	degree 8	$8q - 32q^{2} - 992q^{3} + 5120q^{4} - 11466q^{5} + 34618q^{6} - 54118q^{7} + O(q^{8})$	−	$-1$
23.12.a.b	11	degree 11	$11q + 32q^{2} - 20q^{3} + 11264q^{4} + 1034q^{5} - 22385q^{6} + 159584q^{7} + O(q^{8})$	+	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ generates each orbit's coefficient field; on the newspace its characteristic polynomial factors over $\mathbb{Q}$ as one irreducible factor per orbit:

Orbit	Characteristic polynomial of $T$
23.12.a.a	$x^{8} + 1024x^{7} - 554077x^{6} - 616567378x^{5} + 113277746511x^{4} + 107031122948252x^{3} - 11956604766607619x^{2} - 5301927678130101962x + 722503614756205523600$
23.12.a.b	$x^{11} - 12x^{10} - 1274719x^{9} - 131292363x^{8} + 549872365729x^{7} + 121019089265197x^{6} - 81166447960286183x^{5} - 27245722792085231849x^{4} + 133002797872639003650x^{3} + 410605855091268250301971x^{2} - 22611899694894988018433374x + 326358227706495136860784000$

Dimensions

Newforms $S_{12}^{\mathrm{new}}(\Gamma_0(23))$	19
Old forms	2
Cusp forms $S_{12}(\Gamma_0(23))$	21
Eisenstein series $E_{12}(\Gamma_0(23))$	2
Modular forms $M_{12}(\Gamma_0(23))$	23

Decomposition of the old subspace

$S_{12}^{\mathrm{old}}(\Gamma_0(23)) =$ $S_{12}^{\mathrm{new}}(\Gamma_0(1))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.519 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

dim M^+ at levels [1, 23]: [2, 23] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 19 = 1 x 19 (phi(ord eps) x dim S_k^new); 7 primes, 0 rejected

Open in the notebook · JSON · stored data

Recompute it yourself

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

newform_orbits(23, 12)

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

cargo run --release -p sagebrush-web --example atlas -- 23:12 1000

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