Atlas › Modular forms › Weight 4 › Level 92 › 92.4.a

Newspace 92.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(92))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
92.4.a.a	3	degree 3	$3q - 4q^{3} - 10q^{5} - 46q^{7} + O(q^{8})$	+
92.4.a.b	3	degree 3	$3q + 8q^{3} + 42q^{7} + O(q^{8})$	−

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + T_{5}$ 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 $T$
92.4.a.a	$x^{3} + 14x^{2} - 71x - 1108$
92.4.a.b	$x^{3} - 8x^{2} - 191x + 342$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(92))$	6
Old forms	27
Cusp forms $S_{4}(\Gamma_0(92))$	33
Eisenstein series $E_{4}(\Gamma_0(92))$	6
Modular forms $M_{4}(\Gamma_0(92))$	39

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(92)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(23))^{\oplus 3}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(46))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.106 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, 2, 4, 23, 46, 92]: [1, 2, 3, 7, 20, 39] (certified at ell = 2147483647)
T = [(3, 1), (5, 1)]; h of degree 6 = 1 x 6 (phi(ord eps) x dim S_k^new); 2 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(92, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 92:4 1000

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