Atlas › Modular forms › Weight 2 › Level 152 › 152.2.a

Newspace 152.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(152))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
152.2.a.a	1	$\mathbb{Q}$	$q - 2q^{3} - q^{5} - 3q^{7} + O(q^{8})$	+	152a1 rank 1
152.2.a.b	1	$\mathbb{Q}$	$q + q^{3} + 3q^{7} + O(q^{8})$	−	152b1 rank 0
152.2.a.c	3	degree 3	$3q + q^{3} + q^{5} + 4q^{7} + O(q^{8})$	+

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{5} + 5T_{7} + 7T_{11} + 9T_{13}$ 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 $T$
152.2.a.a	$x + 77$
152.2.a.b	$x - 39$
152.2.a.c	$x^{3} - 34x^{2} - 2291x + 52048$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(152))$	5
Old forms	12
Cusp forms $S_{2}(\Gamma_0(152))$	17
Eisenstein series $E_{2}(\Gamma_0(152))$	7
Modular forms $M_{2}(\Gamma_0(152))$	24

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(152)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(19))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(38))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(76))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.184 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, 8, 19, 38, 76, 152]: [0, 1, 2, 3, 2, 7, 13, 24] (certified at ell = 2147483647)
T = [(3, 1), (5, 3), (7, 5), (11, 7), (13, 9)]; h of degree 5 = 1 x 5 (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(152, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 152:2 1000

← 151.2.a · 153.2.a →