Atlas › Modular forms › Weight 4 › Level 109 › 109.4.a

Newspace 109.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(109))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
109.4.a.a	12	degree 12	$12q - 6q^{2} - 19q^{3} + 36q^{4} - 40q^{5} - 53q^{6} - 32q^{7} + O(q^{8})$	−	$-1$
109.4.a.b	15	degree 15	$15q + 4q^{2} + 17q^{3} + 72q^{4} + 40q^{5} + 31q^{6} + 24q^{7} + O(q^{8})$	+	$+1$

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 $T$
109.4.a.a	$x^{12} + 25x^{11} + 110x^{10} - 1326x^{9} - 9523x^{8} + 14540x^{7} + 174000x^{6} + 5222x^{5} - 933500x^{4} - 75993x^{3} + 1035512x^{2} - 21604x - 125688$
109.4.a.b	$x^{15} - 21x^{14} - 204x^{13} + 6214x^{12} + 5691x^{11} - 681564x^{10} + 1186992x^{9} + 34790152x^{8} - 96195800x^{7} - 858948365x^{6} + 2610615488x^{5} + 9759575116x^{4} - 29172345320x^{3} - 35492139456x^{2} + 116926215616x - 60803961088$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(109))$	27
Old forms	0
Cusp forms $S_{4}(\Gamma_0(109))$	27
Eisenstein series $E_{4}(\Gamma_0(109))$	2
Modular forms $M_{4}(\Gamma_0(109))$	29

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.105 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, 109]: [1, 29] (certified at ell = 2147482801)
T = [(2, 1), (3, 1)]; h of degree 27 = 1 x 27 (phi(ord eps) x dim S_k^new); 4 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(109, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 109:4 1000

← 108.4.a · 110.4.a →