Atlas › Modular forms › Weight 2 › Level 277 › 277.2.a

Newspace 277.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(277))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
277.2.a.a	1	$\mathbb{Q}$	$q + q^{2} - 2q^{3} - q^{4} + 2q^{5} - 2q^{6} - 4q^{7} + O(q^{8})$	+	$-1$	277a1 rank 1
277.2.a.b	3	degree 3	$3q - q^{2} + 6q^{3} + q^{4} + 4q^{5} - 2q^{6} + 4q^{7} + O(q^{8})$	−	$+1$
277.2.a.c	9	degree 9	$9q - 6q^{2} - 10q^{3} + 10q^{4} - 12q^{5} + 3q^{6} - 2q^{7} + O(q^{8})$	+	$-1$
277.2.a.d	9	degree 9	$9q + 4q^{2} + 6q^{3} + 10q^{4} + 4q^{5} + q^{6} - 2q^{7} + O(q^{8})$	−	$+1$

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 $T$
277.2.a.a	$x + 1$
277.2.a.b	$x^{3} - 5x^{2} + 5x + 1$
277.2.a.c	$x^{9} + 16x^{8} + 92x^{7} + 219x^{6} + 145x^{5} - 149x^{4} - 115x^{3} + 51x^{2} + 14x - 5$
277.2.a.d	$x^{9} - 10x^{8} + 16x^{7} + 119x^{6} - 393x^{5} - 133x^{4} + 1575x^{3} - 1317x^{2} - 116x + 137$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(277))$	22
Old forms	0
Cusp forms $S_{2}(\Gamma_0(277))$	22
Eisenstein series $E_{2}(\Gamma_0(277))$	1
Modular forms $M_{2}(\Gamma_0(277))$	23

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.171 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, 277]: [0, 23] (certified at ell = 2147483137)
T = [(2, 1), (3, 1)]; h of degree 22 = 1 x 22 (phi(ord eps) x dim S_k^new); 3 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(277, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 277:2 1000

← 276.2.a · 278.2.a →