Atlas › Modular forms › Weight 2 › Level 223 › 223.2.a

Newspace 223.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(223))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
223.2.a.a	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} - 2q^{3} + 2q^{4} - 4q^{5} + 6q^{6} + O(q^{8})$	+	$-1$
223.2.a.b	4	degree 4	$4q - 4q^{2} + 4q^{4} - 3q^{5} - 8q^{6} - 6q^{7} + O(q^{8})$	+	$-1$
223.2.a.c	12	degree 12	$12q + 7q^{2} + 13q^{4} + 7q^{5} - 4q^{6} + 2q^{7} + O(q^{8})$	−	$+1$

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 $T$
223.2.a.a	$x^{2} + 8x - 16$
223.2.a.b	$x^{4} + 4x^{3} - 10x^{2} - 20x + 9$
223.2.a.c	$x^{12} - 7x^{11} - 225x^{10} + 1623x^{9} + 17746x^{8} - 141078x^{7} - 539762x^{6} + 5440217x^{5} + 2349059x^{4} - 81368851x^{3} + 108730841x^{2} + 159919856x - 167332732$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(223))$	18
Old forms	0
Cusp forms $S_{2}(\Gamma_0(223))$	18
Eisenstein series $E_{2}(\Gamma_0(223))$	1
Modular forms $M_{2}(\Gamma_0(223))$	19

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.173 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, 223]: [0, 19] (certified at ell = 2147482591)
T = [(2, 1), (3, 3)]; h of degree 18 = 1 x 18 (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(223, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 223:2 1000

← 222.2.a · 224.2.a →