Atlas › Modular forms › Weight 4 › Level 235 › 235.4.a

Newspace 235.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(235))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
235.4.a.a	8	degree 8	$8q - 3q^{2} - 10q^{3} + 9q^{4} + 40q^{5} - 42q^{6} - 15q^{7} + O(q^{8})$	− +	$-1$
235.4.a.b	10	degree 10	$10q + 7q^{2} + 8q^{3} + 33q^{4} - 50q^{5} - 2q^{6} + 9q^{7} + O(q^{8})$	+ +	$+1$
235.4.a.c	13	degree 13	$13q - 3q^{2} - 10q^{3} + 53q^{4} - 65q^{5} - 26q^{6} - 19q^{7} + O(q^{8})$	+ −	$-1$
235.4.a.d	15	degree 15	$15q + 7q^{2} + 8q^{3} + 69q^{4} + 75q^{5} + 30q^{6} + 13q^{7} + O(q^{8})$	− −	$+1$

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 $T$
235.4.a.a	$x^{8} + 13x^{7} - 25x^{6} - 739x^{5} - 105x^{4} + 15193x^{3} + 186x^{2} - 115960x + 94728$
235.4.a.b	$x^{10} - 15x^{9} - 121x^{8} + 2069x^{7} + 4393x^{6} - 83111x^{5} - 98254x^{4} + 1023826x^{3} + 1832044x^{2} - 1320544x - 2818384$
235.4.a.c	$x^{13} + 13x^{12} - 210x^{11} - 2400x^{10} + 19679x^{9} + 147838x^{8} - 995119x^{7} - 2943679x^{6} + 22534962x^{5} - 1051126x^{4} - 153632113x^{3} + 255419122x^{2} - 146304104x + 26398040$
235.4.a.d	$x^{15} - 15x^{14} - 334x^{13} + 5320x^{12} + 35389x^{11} - 617554x^{10} - 1737293x^{9} + 31289583x^{8} + 48110844x^{7} - 691894342x^{6} - 807265985x^{5} + 5327365336x^{4} + 5288905670x^{3} - 12081352468x^{2} - 6162319520x + 6932606800$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(235))$	46
Old forms	24
Cusp forms $S_{4}(\Gamma_0(235))$	70
Eisenstein series $E_{4}(\Gamma_0(235))$	4
Modular forms $M_{4}(\Gamma_0(235))$	74

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(235)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(5))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(47))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.147 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, 47, 235]: [1, 3, 13, 74] (certified at ell = 2147483137)
T = [(2, 1), (3, 1)]; h of degree 46 = 1 x 46 (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(235, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 235:4 1000

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