Atlas › Modular forms › Weight 2 › Level 795 › 795.2.a

Newspace 795.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(795))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
795.2.a.a	1	$\mathbb{Q}$	$q - q^{3} - 2q^{4} - q^{5} - 2q^{7} + O(q^{8})$	+ + −	$+1$	795b1 rank 0
795.2.a.b	1	$\mathbb{Q}$	$q + q^{3} - 2q^{4} - q^{5} + 2q^{7} + O(q^{8})$	− + +	$+1$	795c1 rank 0
795.2.a.c	1	$\mathbb{Q}$	$q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} + 4q^{7} + O(q^{8})$	+ + +	$-1$	795a1 rank 1
795.2.a.d	1	$\mathbb{Q}$	$q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} + O(q^{8})$	− + +	$+1$	795d1 rank 0
795.2.a.e	3	degree 3	$3q - 3q^{2} + 3q^{3} + 3q^{4} + 3q^{5} - 3q^{6} - 9q^{7} + O(q^{8})$	− − +	$-1$
795.2.a.f	3	degree 3	$3q - q^{2} - 3q^{3} + 3q^{4} - 3q^{5} + q^{6} + q^{7} + O(q^{8})$	+ + +	$-1$
795.2.a.g	3	degree 3	$3q - q^{2} + 3q^{3} - q^{4} - 3q^{5} - q^{6} - 5q^{7} + O(q^{8})$	− + −	$-1$
795.2.a.h	3	degree 3	$3q + q^{2} - 3q^{3} + 3q^{4} - 3q^{5} - q^{6} - 5q^{7} + O(q^{8})$	+ + −	$+1$
795.2.a.i	4	degree 4	$4q - 4q^{2} - 4q^{3} + 6q^{4} + 4q^{5} + 4q^{6} + q^{7} + O(q^{8})$	+ − −	$-1$
795.2.a.j	4	degree 4	$4q + 3q^{2} - 4q^{3} + 5q^{4} + 4q^{5} - 3q^{6} - 3q^{7} + O(q^{8})$	+ − +	$+1$
795.2.a.k	5	degree 5	$5q - q^{2} + 5q^{3} + 13q^{4} - 5q^{5} - q^{6} + 9q^{7} + O(q^{8})$	− + +	$+1$
795.2.a.l	6	degree 6	$6q + q^{2} + 6q^{3} + 7q^{4} + 6q^{5} + q^{6} + 7q^{7} + O(q^{8})$	− − −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{7}$ 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 $T$
795.2.a.a	$x + 6$
795.2.a.b	$x - 6$
795.2.a.c	$x - 13$
795.2.a.d	$x - 1$
795.2.a.e	$x^{3} + 30x^{2} + 216x + 24$
795.2.a.f	$x^{3} - 2x^{2} - 16x + 24$
795.2.a.g	$x^{3} + 16x^{2} + 76x + 104$
795.2.a.h	$x^{3} + 14x^{2} - 4x - 120$
795.2.a.i	$x^{4} + x^{3} - 92x^{2} - 340x + 8$
795.2.a.j	$x^{4} + 6x^{3} - 140x^{2} - 96x + 368$
795.2.a.k	$x^{5} - 26x^{4} + 49x^{3} + 3432x^{2} - 29552x + 67776$
795.2.a.l	$x^{6} - 22x^{5} + 21x^{4} + 1976x^{3} - 7404x^{2} - 32808x + 98192$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(795))$	35
Old forms	70
Cusp forms $S_{2}(\Gamma_0(795))$	105
Eisenstein series $E_{2}(\Gamma_0(795))$	7
Modular forms $M_{2}(\Gamma_0(795))$	112

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(795)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(15))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(53))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(159))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(265))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.309 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, 3, 5, 15, 53, 159, 265, 795]: [0, 1, 1, 4, 5, 20, 28, 112] (certified at ell = 2147483053)
T = [(2, 1), (7, 3)]; h of degree 35 = 1 x 35 (phi(ord eps) x dim S_k^new); 6 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(795, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 795:2 1000

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