Atlas › Modular forms › Weight 4 › Level 97 › 97.4.a

Newspace 97.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(97))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
97.4.a.a	11	degree 11	$11q - 11q^{2} - 12q^{3} + 35q^{4} - 34q^{5} - 37q^{6} - 68q^{7} + O(q^{8})$	−	$-1$
97.4.a.b	13	degree 13	$13q + 9q^{2} + 12q^{3} + 59q^{4} + 16q^{5} + 11q^{6} + 58q^{7} + O(q^{8})$	+	$+1$

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 $T$
97.4.a.a	$x^{11} + 23x^{10} + 53x^{9} - 1557x^{8} - 5734x^{7} + 28560x^{6} + 93398x^{5} - 214122x^{4} - 474120x^{3} + 599054x^{2} + 676141x - 250821$
97.4.a.b	$x^{13} - 21x^{12} - 131x^{11} + 4979x^{10} - 5182x^{9} - 421768x^{8} + 1458286x^{7} + 15168102x^{6} - 73180372x^{5} - 198084542x^{4} + 1252624925x^{3} + 198233487x^{2} - 4445148108x - 1187069816$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(97))$	24
Old forms	0
Cusp forms $S_{4}(\Gamma_0(97))$	24
Eisenstein series $E_{4}(\Gamma_0(97))$	2
Modular forms $M_{4}(\Gamma_0(97))$	26

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.101 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, 97]: [1, 26] (certified at ell = 2147483137)
T = [(2, 1), (3, 1)]; h of degree 24 = 1 x 24 (phi(ord eps) x dim S_k^new); 4 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(97, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 97:4 1000

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