Atlas › Modular forms › Weight 4 › Level 127 › 127.4.a

Newspace 127.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(127))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
127.4.a.a	1	$\mathbb{Q}$	$q - q^{2} - 8q^{3} - 7q^{4} - 15q^{5} + 8q^{6} - 25q^{7} + O(q^{8})$	+	$+1$
127.4.a.b	13	degree 13	$13q - 8q^{2} - 16q^{3} + 34q^{4} - 46q^{5} - 2q^{6} - 26q^{7} + O(q^{8})$	−	$-1$
127.4.a.c	17	degree 17	$17q + 9q^{2} + 22q^{3} + 81q^{4} + 69q^{5} + 26q^{6} + 55q^{7} + O(q^{8})$	+	$+1$

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 $T$
127.4.a.a	$x + 9$
127.4.a.b	$x^{13} + 24x^{12} + 44x^{11} - 2104x^{10} - 8153x^{9} + 58690x^{8} + 267426x^{7} - 567203x^{6} - 2973938x^{5} + 1589288x^{4} + 11202964x^{3} + 15981x^{2} - 8708440x - 34772$
127.4.a.c	$x^{17} - 31x^{16} + 21x^{15} + 7971x^{14} - 55846x^{13} - 752735x^{12} + 8286587x^{11} + 28837526x^{10} - 537189110x^{9} - 71778389x^{8} + 17686772875x^{7} - 25528604560x^{6} - 287781173457x^{5} + 644721219507x^{4} + 1904757844993x^{3} - 4811436431847x^{2} - 1606766330658x + 1622846153868$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(127))$	31
Old forms	0
Cusp forms $S_{4}(\Gamma_0(127))$	31
Eisenstein series $E_{4}(\Gamma_0(127))$	2
Modular forms $M_{4}(\Gamma_0(127))$	33

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.109 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, 127]: [1, 33] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 31 = 1 x 31 (phi(ord eps) x dim S_k^new); 5 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(127, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 127:4 1000

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