Atlas › Modular forms › Weight 4 › Level 103 › 103.4.a

Newspace 103.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(103))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
103.4.a.a	10	degree 10	$10q - 11q^{2} - 8q^{3} + 27q^{4} - 30q^{5} - 17q^{6} - 33q^{7} + O(q^{8})$	−	$-1$
103.4.a.b	15	degree 15	$15q + 9q^{2} + 10q^{3} + 67q^{4} + 30q^{5} + 19q^{6} + 23q^{7} + O(q^{8})$	+	$+1$

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 $T$
103.4.a.a	$x^{10} + 19x^{9} + 21x^{8} - 936x^{7} - 2024x^{6} + 15022x^{5} + 33595x^{4} - 93071x^{3} - 205527x^{2} + 186260x + 406092$
103.4.a.b	$x^{15} - 19x^{14} - 235x^{13} + 5688x^{12} + 17192x^{11} - 674833x^{10} - 11640x^{9} + 39825892x^{8} - 56891893x^{7} - 1189103692x^{6} + 2697205904x^{5} + 15632995657x^{4} - 43342961141x^{3} - 50676583433x^{2} + 129132221816x + 70653529840$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(103))$	25
Old forms	0
Cusp forms $S_{4}(\Gamma_0(103))$	25
Eisenstein series $E_{4}(\Gamma_0(103))$	2
Modular forms $M_{4}(\Gamma_0(103))$	27

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.102 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, 103]: [1, 27] (certified at ell = 2147482501)
T = [(2, 1), (3, 1)]; h of degree 25 = 1 x 25 (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(103, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 103:4 1000

← 102.4.a · 104.4.a →