Atlas › Modular forms › Weight 2 › Level 835 › 835.2.a

Newspace 835.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(835))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
835.2.a.a	6	degree 6	$6q - 2q^{2} - 3q^{3} + 6q^{5} + q^{6} - q^{7} + O(q^{8})$	− −	$-1$
835.2.a.b	11	degree 11	$11q + 2q^{2} + 3q^{3} + 8q^{4} - 11q^{5} + q^{6} + q^{7} + O(q^{8})$	+ −	$+1$
835.2.a.c	16	degree 16	$16q - 5q^{2} - 7q^{3} + 15q^{4} - 16q^{5} - 3q^{6} - 7q^{7} + O(q^{8})$	+ +	$-1$
835.2.a.d	22	degree 22	$22q + 2q^{2} + 3q^{3} + 30q^{4} + 22q^{5} + 9q^{6} - q^{7} + O(q^{8})$	− +	$+1$

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 $T$
835.2.a.a	$x^{6} + 5x^{5} + x^{4} - 16x^{3} - 6x^{2} + 7x - 1$
835.2.a.b	$x^{11} - 5x^{10} - 24x^{9} + 113x^{8} + 227x^{7} - 809x^{6} - 977x^{5} + 1857x^{4} + 1085x^{3} - 1658x^{2} - 40x + 248$
835.2.a.c	$x^{16} + 12x^{15} + 22x^{14} - 219x^{13} - 755x^{12} + 1318x^{11} + 6486x^{10} - 3380x^{9} - 24657x^{8} + 4481x^{7} + 45760x^{6} - 6120x^{5} - 39982x^{4} + 6958x^{3} + 13158x^{2} - 1691x - 1399$
835.2.a.d	$x^{22} - 5x^{21} - 87x^{20} + 470x^{19} + 2794x^{18} - 17064x^{17} - 40308x^{16} + 309899x^{15} + 213551x^{14} - 3000568x^{13} + 728032x^{12} + 15067444x^{11} - 12509763x^{10} - 34050310x^{9} + 45184448x^{8} + 16787179x^{7} - 48831906x^{6} + 22371376x^{5} - 216026x^{4} - 1780827x^{3} + 212378x^{2} + 20776x + 392$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(835))$	55
Old forms	28
Cusp forms $S_{2}(\Gamma_0(835))$	83
Eisenstein series $E_{2}(\Gamma_0(835))$	3
Modular forms $M_{2}(\Gamma_0(835))$	86

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(835)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(167))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.247 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, 167, 835]: [0, 1, 15, 86] (certified at ell = 2147483237)
T = [(2, 1), (3, 1)]; h of degree 55 = 1 x 55 (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(835, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 835:2 1000

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