Atlas › Modular forms › Weight 2 › Level 895 › 895.2.a

Newspace 895.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(895))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
895.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + O(q^{8})$	+ +	$-1$	895a1 rank 1
895.2.a.b	1	$\mathbb{Q}$	$q - q^{2} + 3q^{3} - q^{4} - q^{5} - 3q^{6} - 4q^{7} + O(q^{8})$	+ −	$+1$	895b1 rank 0
895.2.a.c	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} + 2q^{3} + 2q^{4} - 2q^{5} + 2q^{6} + O(q^{8})$	+ +	$-1$
895.2.a.d	8	degree 8	$8q - q^{2} - 3q^{3} + 5q^{4} - 8q^{5} - 5q^{6} - 2q^{7} + O(q^{8})$	+ +	$-1$
895.2.a.e	11	degree 11	$11q - 6q^{2} - 4q^{3} + 10q^{4} + 11q^{5} - 2q^{6} - 10q^{7} + O(q^{8})$	− −	$-1$
895.2.a.f	18	degree 18	$18q + 7q^{2} - 3q^{3} + 23q^{4} - 18q^{5} + 13q^{6} + O(q^{8})$	+ −	$+1$
895.2.a.g	18	degree 18	$18q + 7q^{2} + 4q^{3} + 19q^{4} + 18q^{5} + 12q^{7} + O(q^{8})$	− +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3} + 5T_{7} + 7T_{11}$ 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 $T$
895.2.a.a	$x - 23$
895.2.a.b	$x + 5$
895.2.a.c	$x^{2} + 10x - 47$
895.2.a.d	$x^{8} + 132x^{7} + 6594x^{6} + 147709x^{5} + 1050856x^{4} - 14168047x^{3} - 302711306x^{2} - 1859728751x - 3767597231$
895.2.a.e	$x^{11} + 117x^{10} + 3847x^{9} - 23824x^{8} - 3024017x^{7} - 17880376x^{6} + 866722170x^{5} + 6818328082x^{4} - 118604089307x^{3} - 715028646388x^{2} + 6749891272350x + 14090561706841$
895.2.a.f	$x^{18} - 110x^{17} - 4213x^{16} + 918833x^{15} - 16434072x^{14} - 2164857150x^{13} + 84726528918x^{12} + 1807078326562x^{11} - 132319155799468x^{10} + 113870911349733x^{9} + 96018431523887336x^{8} - 1061750455780271693x^{7} - 32531756484656953766x^{6} + 617840586698701060528x^{5} + 3495377685071056841172x^{4} - 129778599023917311122306x^{3} + 358731261604465608348899x^{2} + 6636977606272453860234519x - 33840233262798879688595795$
895.2.a.g	$x^{18} - 170x^{17} + 7193x^{16} + 303693x^{15} - 30676452x^{14} + 320911288x^{13} + 34466135600x^{12} - 987184404628x^{11} - 10009598712030x^{10} + 693573289572363x^{9} - 4063881921358306x^{8} - 170284407225287487x^{7} + 2335533698932688994x^{6} + 10858690264348221938x^{5} - 332001187446964218610x^{4} + 830270162063493070264x^{3} + 13408545807770393546469x^{2} - 75024107685370235138789x + 56535536270500133211613$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(895))$	59
Old forms	30
Cusp forms $S_{2}(\Gamma_0(895))$	89
Eisenstein series $E_{2}(\Gamma_0(895))$	3
Modular forms $M_{2}(\Gamma_0(895))$	92

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(895)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(179))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.429 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, 179, 895]: [0, 1, 16, 92] (certified at ell = 2147483137)
T = [(2, 1), (3, 3), (7, 5), (11, 7)]; h of degree 59 = 1 x 59 (phi(ord eps) x dim S_k^new); 13 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(895, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 895:2 1000

← 894.2.a · 896.2.a →