Atlas › Modular forms › Weight 2 › Level 433 › 433.2.a

Newspace 433.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(433))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
433.2.a.a	1	$\mathbb{Q}$	$q - q^{2} - 2q^{3} - q^{4} - 4q^{5} + 2q^{6} - 3q^{7} + O(q^{8})$	−	$+1$	433a1 rank 2
433.2.a.b	3	degree 3	$3q + 3q^{2} - 3q^{4} + 7q^{7} + O(q^{8})$	−	$+1$
433.2.a.c	15	degree 15	$15q - 10q^{2} - 8q^{3} + 12q^{4} - 5q^{5} + q^{6} - 15q^{7} + O(q^{8})$	+	$-1$
433.2.a.d	16	degree 16	$16q + 7q^{2} + 6q^{3} + 27q^{4} + 7q^{5} - q^{6} + 7q^{7} + O(q^{8})$	−	$+1$

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 $T$
433.2.a.a	$x + 3$
433.2.a.b	$x^{3} - 3x^{2} - 5x + 11$
433.2.a.c	$x^{15} + 18x^{14} + 115x^{13} + 237x^{12} - 532x^{11} - 2987x^{10} - 2184x^{9} + 8027x^{8} + 13096x^{7} - 3756x^{6} - 16393x^{5} - 3891x^{4} + 5893x^{3} + 1865x^{2} - 476x + 23$
433.2.a.d	$x^{16} - 13x^{15} + 25x^{14} + 328x^{13} - 1499x^{12} - 1295x^{11} + 16641x^{10} - 11749x^{9} - 71809x^{8} + 96032x^{7} + 128699x^{6} - 227616x^{5} - 82858x^{4} + 185074x^{3} + 29413x^{2} - 46005x - 11233$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(433))$	35
Old forms	0
Cusp forms $S_{2}(\Gamma_0(433))$	35
Eisenstein series $E_{2}(\Gamma_0(433))$	1
Modular forms $M_{2}(\Gamma_0(433))$	36

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.271 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, 433]: [0, 36] (certified at ell = 2147482801)
T = [(2, 1), (3, 1)]; h of degree 35 = 1 x 35 (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(433, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 433:2 1000

← 432.2.a · 434.2.a →