Atlas › Modular forms › Weight 2 › Level 929 › 929.2.a

Newspace 929.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(929))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
929.2.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q - 3q^{2} + 3q^{4} - q^{5} - 5q^{6} - 3q^{7} + O(q^{8})$	+	$-1$
929.2.a.b	28	degree 28	$28q - q^{2} - 5q^{3} + 13q^{4} - 7q^{5} - 7q^{6} - 32q^{7} + O(q^{8})$	+	$-1$
929.2.a.c	47	degree 47	$47q + 3q^{2} + 3q^{3} + 63q^{4} + 2q^{5} + 6q^{6} + 39q^{7} + O(q^{8})$	−	$+1$

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 $T$
929.2.a.a	$x^{2} + 3x + 1$
929.2.a.b	$x^{28} + 6x^{27} - 57x^{26} - 353x^{25} + 1431x^{24} + 8720x^{23} - 22110x^{22} - 120242x^{21} + 239682x^{20} + 1020060x^{19} - 1882048x^{18} - 5465500x^{17} + 10442420x^{16} + 18072375x^{15} - 39020930x^{14} - 33691597x^{13} + 92665084x^{12} + 25845870x^{11} - 130677463x^{10} + 11983188x^{9} + 101440308x^{8} - 33712932x^{7} - 37713277x^{6} + 20062121x^{5} + 3689498x^{4} - 3835865x^{3} + 735427x^{2} - 51799x + 1147$
929.2.a.c	$x^{47} - 6x^{46} - 165x^{45} + 1046x^{44} + 12026x^{43} - 81513x^{42} - 511194x^{41} + 3764305x^{40} + 14101679x^{39} - 115245495x^{38} - 266016583x^{37} + 2481781385x^{36} + 3527337352x^{35} - 38966166377x^{34} - 33367256492x^{33} + 456686572553x^{32} + 227907145591x^{31} - 4059522659741x^{30} - 1158080264548x^{29} + 27653364280651x^{28} + 4830712098971x^{27} - 145138274961293x^{26} - 20137240560897x^{25} + 587205364277733x^{24} + 90844624880920x^{23} - 1823094513072909x^{22} - 369899431001629x^{21} + 4302955860054386x^{20} + 1143939832047744x^{19} - 7617412486450295x^{18} - 2501577889898149x^{17} + 9953785003797272x^{16} + 3762339838190752x^{15} - 9446528496191357x^{14} - 3822103897594547x^{13} + 6415629833745829x^{12} + 2568417251258710x^{11} - 3073214937487960x^{10} - 1103718649364606x^{9} + 1017507106759046x^{8} + 284444574106092x^{7} - 223431798842140x^{6} - 38173647931964x^{5} + 29558672724648x^{4} + 1716214031600x^{3} - 1870426745648x^{2} + 34555885272x + 31739480792$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(929))$	77
Old forms	0
Cusp forms $S_{2}(\Gamma_0(929))$	77
Eisenstein series $E_{2}(\Gamma_0(929))$	1
Modular forms $M_{2}(\Gamma_0(929))$	78

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.291 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, 929]: [0, 78] (certified at ell = 2147480161)
T = [(2, 1), (3, 1)]; h of degree 77 = 1 x 77 (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(929, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 929:2 1000

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