Atlas › Modular forms › Weight 4 › Level 141 › 141.4.a

Newspace 141.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(141))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
141.4.a.a	2	$\mathbb{Q}(\sqrt{111})$	$2q + 8q^{2} + 6q^{3} + 16q^{4} + 6q^{5} + 24q^{6} + 20q^{7} + O(q^{8})$	− −	$+1$
141.4.a.b	5	degree 5	$5q - 5q^{2} + 15q^{3} + 7q^{4} - 34q^{5} - 15q^{6} - 26q^{7} + O(q^{8})$	− +	$-1$
141.4.a.c	5	degree 5	$5q - q^{2} + 15q^{3} + 15q^{4} + 10q^{5} - 3q^{6} + 10q^{7} + O(q^{8})$	− −	$+1$
141.4.a.d	5	degree 5	$5q + q^{2} - 15q^{3} + 11q^{4} - 4q^{5} - 3q^{6} - 26q^{7} + O(q^{8})$	+ −	$-1$
141.4.a.e	7	degree 7	$7q - 3q^{2} - 21q^{3} + 35q^{4} + 6q^{5} + 9q^{6} + 30q^{7} + O(q^{8})$	+ +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{5}$ 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 $T$
141.4.a.a	$x^{2} - 14x - 62$
141.4.a.b	$x^{5} + 39x^{4} + 344x^{3} - 3004x^{2} - 53505x - 174563$
141.4.a.c	$x^{5} - 9x^{4} - 434x^{3} + 4342x^{2} + 1341x - 48353$
141.4.a.d	$x^{5} + 3x^{4} - 190x^{3} - 254x^{2} + 1473x + 239$
141.4.a.e	$x^{7} - 3x^{6} - 672x^{5} + 3282x^{4} + 141579x^{3} - 864453x^{2} - 9055660x + 60233310$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(141))$	24
Old forms	22
Cusp forms $S_{4}(\Gamma_0(141))$	46
Eisenstein series $E_{4}(\Gamma_0(141))$	4
Modular forms $M_{4}(\Gamma_0(141))$	50

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(141)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(47))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.117 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, 3, 47, 141]: [1, 2, 13, 50] (certified at ell = 2147483137)
T = [(2, 1), (5, 1)]; h of degree 24 = 1 x 24 (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(141, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 141:4 1000

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