Atlas › Modular forms › Weight 2 › Level 179 › 179.2.a

Newspace 179.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(179))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
179.2.a.a	1	$\mathbb{Q}$	$q + 2q^{2} + 2q^{4} + 3q^{5} - 4q^{7} + O(q^{8})$	−	$+1$	179a1 rank 0
179.2.a.b	3	degree 3	$3q - q^{2} - 2q^{3} - q^{4} - 4q^{5} - 4q^{6} - 4q^{7} + O(q^{8})$	+	$-1$
179.2.a.c	11	degree 11	$11q - 3q^{2} + 15q^{4} + 3q^{5} + 8q^{7} + O(q^{8})$	−	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3}$ 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 $T$
179.2.a.a	$x - 2$
179.2.a.b	$x^{3} + 7x^{2} + 7x - 7$
179.2.a.c	$x^{11} + 3x^{10} - 239x^{9} - 393x^{8} + 20243x^{7} + 5727x^{6} - 697741x^{5} + 723929x^{4} + 7783031x^{3} - 20774523x^{2} + 16802057x - 3985159$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(179))$	15
Old forms	0
Cusp forms $S_{2}(\Gamma_0(179))$	15
Eisenstein series $E_{2}(\Gamma_0(179))$	1
Modular forms $M_{2}(\Gamma_0(179))$	16

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.164 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, 179]: [0, 16] (certified at ell = 2147483137)
T = [(2, 1), (3, 3)]; h of degree 15 = 1 x 15 (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(179, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 179:2 1000

← 178.2.a · 180.2.a →