Atlas › Modular forms › Weight 4 › Level 107 › 107.4.a

Newspace 107.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(107))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
107.4.a.a	10	degree 10	$10q - 2q^{2} - 17q^{3} + 20q^{4} - 31q^{5} - 39q^{6} - 44q^{7} + O(q^{8})$	−	$-1$
107.4.a.b	16	degree 16	$16q + 4q^{2} + 13q^{3} + 80q^{4} + 39q^{5} + 9q^{6} + 68q^{7} + O(q^{8})$	+	$+1$

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 $T$
107.4.a.a	$x^{10} + 19x^{9} + 21x^{8} - 1030x^{7} - 2819x^{6} + 13327x^{5} + 40797x^{4} - 22536x^{3} - 90676x^{2} + 5184x + 44752$
107.4.a.b	$x^{16} - 17x^{15} - 279x^{14} + 5330x^{13} + 30324x^{12} - 673834x^{11} - 1560379x^{10} + 44012893x^{9} + 31646572x^{8} - 1577181469x^{7} + 332845590x^{6} + 29979347727x^{5} - 24358448723x^{4} - 255574842790x^{3} + 283431673162x^{2} + 472313926916x + 9713514088$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(107))$	26
Old forms	0
Cusp forms $S_{4}(\Gamma_0(107))$	26
Eisenstein series $E_{4}(\Gamma_0(107))$	2
Modular forms $M_{4}(\Gamma_0(107))$	28

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.104 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, 107]: [1, 28] (certified at ell = 2147482621)
T = [(2, 1), (3, 1)]; h of degree 26 = 1 x 26 (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(107, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 107:4 1000

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