Atlas › Modular forms › Weight 4 › Level 148 › 148.4.a

Newspace 148.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(148))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
148.4.a.a	4	degree 4	$4q - q^{3} - 19q^{5} - 6q^{7} + O(q^{8})$	+
148.4.a.b	5	degree 5	$5q - q^{3} + 21q^{5} + 22q^{7} + O(q^{8})$	−

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + T_{5}$ 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 $T$
148.4.a.a	$x^{4} + 20x^{3} + 62x^{2} - 148x - 479$
148.4.a.b	$x^{5} - 20x^{4} - 524x^{3} + 10346x^{2} + 29627x - 781318$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(148))$	9
Old forms	45
Cusp forms $S_{4}(\Gamma_0(148))$	54
Eisenstein series $E_{4}(\Gamma_0(148))$	6
Modular forms $M_{4}(\Gamma_0(148))$	60

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(148)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(37))^{\oplus 3}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(74))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.114 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, 2, 4, 37, 74, 148]: [1, 2, 3, 11, 31, 60] (certified at ell = 2147483629)
T = [(3, 1), (5, 1)]; h of degree 9 = 1 x 9 (phi(ord eps) x dim S_k^new); 2 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(148, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 148:4 1000

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