Atlas › Modular forms › Weight 2 › Level 911 › 911.2.a

Newspace 911.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(911))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
911.2.a.a	9	degree 9	$9q - 5q^{2} + q^{3} + 3q^{4} - q^{5} + 2q^{6} + 5q^{7} + O(q^{8})$	+	$-1$
911.2.a.b	14	degree 14	$14q + 2q^{2} - 7q^{3} + 8q^{4} - 7q^{5} - 13q^{6} - 15q^{7} + O(q^{8})$	+	$-1$
911.2.a.c	53	degree 53	$53q + 2q^{2} + 6q^{3} + 66q^{4} + 10q^{5} + 17q^{6} + 14q^{7} + O(q^{8})$	−	$+1$

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 $T$
911.2.a.a	$x^{9} + 4x^{8} - 14x^{7} - 44x^{6} + 74x^{5} + 134x^{4} - 151x^{3} - 145x^{2} + 90x + 59$
911.2.a.b	$x^{14} + 5x^{13} - 17x^{12} - 103x^{11} + 82x^{10} + 717x^{9} - 170x^{8} - 2261x^{7} + 437x^{6} + 3469x^{5} - 1143x^{4} - 2255x^{3} + 1153x^{2} + 260x - 167$
911.2.a.c	$x^{53} - 8x^{52} - 190x^{51} + 1646x^{50} + 16001x^{49} - 153631x^{48} - 785649x^{47} + 8645993x^{46} + 24752198x^{45} - 328943611x^{44} - 511718334x^{43} + 8991321710x^{42} + 6490683487x^{41} - 183174562967x^{40} - 29373009111x^{39} + 2847428420015x^{38} - 652958181159x^{37} - 34292006238830x^{36} + 17243535850666x^{35} + 322968591001636x^{34} - 224103954202472x^{33} - 2390277296968724x^{32} + 1970619629531648x^{31} + 13913182372815715x^{30} - 12662201359347269x^{29} - 63504653413188194x^{28} + 61155645028061658x^{27} + 225707032570010839x^{26} - 224265121263079304x^{25} - 617438605477097764x^{24} + 624618659829086036x^{23} + 1277583378902561936x^{22} - 1312089849777179121x^{21} - 1949476123407312982x^{20} + 2049275375925845884x^{19} + 2112496229319094176x^{18} - 2324488308358379506x^{17} - 1529974228132608945x^{16} + 1845872229727455001x^{15} + 659103143185166977x^{14} - 968976677029574406x^{13} - 118335133776544227x^{12} + 306750865693429779x^{11} - 15319602267798499x^{10} - 50328244492228539x^{9} + 8135142817585598x^{8} + 3436707949688009x^{7} - 830003386881494x^{6} - 56947690521566x^{5} + 26967770716802x^{4} - 1500239509621x^{3} - 123843165530x^{2} + 14159727911x - 350223237$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(911))$	76
Old forms	0
Cusp forms $S_{2}(\Gamma_0(911))$	76
Eisenstein series $E_{2}(\Gamma_0(911))$	1
Modular forms $M_{2}(\Gamma_0(911))$	77

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.292 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, 911]: [0, 77] (certified at ell = 2147480791)
T = [(2, 1), (3, 1)]; h of degree 76 = 1 x 76 (phi(ord eps) x dim S_k^new); 8 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(911, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 911:2 1000

← 910.2.a · 912.2.a →