Atlas › Modular forms › Weight 4 › Level 95 › 95.4.a

Newspace 95.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(95))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
95.4.a.a	1	$\mathbb{Q}$	$q + 4q^{3} - 8q^{4} - 5q^{5} - 22q^{7} + O(q^{8})$	+ −	$-1$
95.4.a.b	1	$\mathbb{Q}$	$q + 3q^{2} - 5q^{3} + q^{4} - 5q^{5} - 15q^{6} - q^{7} + O(q^{8})$	+ −	$-1$
95.4.a.c	1	$\mathbb{Q}$	$q + 3q^{2} + 7q^{3} + q^{4} + 5q^{5} + 21q^{6} + 11q^{7} + O(q^{8})$	− −	$+1$
95.4.a.d	1	$\mathbb{Q}$	$q + 5q^{2} + 4q^{3} + 17q^{4} + 5q^{5} + 20q^{6} - 32q^{7} + O(q^{8})$	− −	$+1$
95.4.a.e	3	degree 3	$3q - 3q^{2} - 11q^{3} + q^{4} + 15q^{5} + 25q^{6} - 5q^{7} + O(q^{8})$	− +	$-1$
95.4.a.f	5	degree 5	$5q - 3q^{2} - 4q^{3} + 15q^{4} + 25q^{5} - 44q^{6} + 72q^{7} + O(q^{8})$	− −	$+1$
95.4.a.g	6	degree 6	$6q - q^{2} + 5q^{3} + 25q^{4} - 30q^{5} + 61q^{6} + 5q^{7} + O(q^{8})$	+ +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3}$ 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 $T$
95.4.a.a	$x - 12$
95.4.a.b	$x + 12$
95.4.a.c	$x - 24$
95.4.a.d	$x - 17$
95.4.a.e	$x^{3} + 36x^{2} + 250x + 136$
95.4.a.f	$x^{5} + 15x^{4} - 593x^{3} - 5131x^{2} + 27496x + 139454$
95.4.a.g	$x^{6} - 14x^{5} - 1458x^{4} + 13206x^{3} + 603493x^{2} - 2106538x - 59431232$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(95))$	18
Old forms	10
Cusp forms $S_{4}(\Gamma_0(95))$	28
Eisenstein series $E_{4}(\Gamma_0(95))$	4
Modular forms $M_{4}(\Gamma_0(95))$	32

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(95)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(5))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(19))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.11 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, 5, 19, 95]: [1, 3, 6, 32] (certified at ell = 2147483629)
T = [(2, 1), (3, 3)]; h of degree 18 = 1 x 18 (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(95, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 95:4 1000

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