Atlas › Modular forms › Weight 4 › Level 94 › 94.4.a

Newspace 94.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(94))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
94.4.a.a	2	$\mathbb{Q}(\sqrt{85})$	$2q - 4q^{2} - q^{3} + 8q^{4} - 10q^{5} + 2q^{6} + 9q^{7} + O(q^{8})$	+ −	$-1$
94.4.a.b	2	$\mathbb{Q}(\sqrt{5})$	$2q + 4q^{2} - 9q^{3} + 8q^{4} - 20q^{5} - 18q^{6} - 19q^{7} + O(q^{8})$	− +	$-1$
94.4.a.c	4	degree 4	$4q - 8q^{2} - q^{3} + 16q^{4} + 10q^{5} + 2q^{6} - 19q^{7} + O(q^{8})$	+ +	$+1$
94.4.a.d	4	degree 4	$4q + 8q^{2} + 3q^{3} + 16q^{4} + 10q^{5} + 6q^{6} + 37q^{7} + O(q^{8})$	− −	$+1$

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 $T$
94.4.a.a	$x^{2} + 11x + 9$
94.4.a.b	$x^{2} + 29x + 149$
94.4.a.c	$x^{4} - 9x^{3} - 677x^{2} + 5222x - 8236$
94.4.a.d	$x^{4} - 13x^{3} - 129x^{2} + 698x + 2350$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(94))$	12
Old forms	22
Cusp forms $S_{4}(\Gamma_0(94))$	34
Eisenstein series $E_{4}(\Gamma_0(94))$	4
Modular forms $M_{4}(\Gamma_0(94))$	38

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(94)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(47))^{\oplus 2}$

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, 47, 94]: [1, 2, 13, 38] (certified at ell = 2147483137)
T = [(3, 1), (5, 1)]; h of degree 12 = 1 x 12 (phi(ord eps) x dim S_k^new); 3 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(94, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 94:4 1000

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