Atlas › Modular forms › Weight 4 › Level 113 › 113.4.a

Newspace 113.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(113))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
113.4.a.a	12	degree 12	$12q - 4q^{2} - 18q^{3} + 32q^{4} - 24q^{5} - 55q^{6} - 106q^{7} + O(q^{8})$	−	$-1$
113.4.a.b	16	degree 16	$16q + 4q^{2} + 18q^{3} + 80q^{4} + 6q^{5} + 5q^{6} + 118q^{7} + O(q^{8})$	+	$+1$

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 $T$
113.4.a.a	$x^{12} + 22x^{11} + 36x^{10} - 1480x^{9} - 4684x^{8} + 28734x^{7} + 71925x^{6} - 239624x^{5} - 281328x^{4} + 855224x^{3} - 77149x^{2} - 461316x + 146871$
113.4.a.b	$x^{16} - 22x^{15} - 172x^{14} + 6232x^{13} + 1358x^{12} - 710592x^{11} + 1624301x^{10} + 41048618x^{9} - 148306138x^{8} - 1221899220x^{7} + 5739235325x^{6} + 15809390778x^{5} - 102632606019x^{4} - 11121966262x^{3} + 652152347414x^{2} - 877473442564x + 224073281402$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(113))$	28
Old forms	0
Cusp forms $S_{4}(\Gamma_0(113))$	28
Eisenstein series $E_{4}(\Gamma_0(113))$	2
Modular forms $M_{4}(\Gamma_0(113))$	30

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.106 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, 113]: [1, 30] (certified at ell = 2147480161)
T = [(2, 1), (3, 1)]; h of degree 28 = 1 x 28 (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(113, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 113:4 1000

← 112.4.a · 114.4.a →