Atlas › Modular forms › Weight 2 › Level 199 › 199.2.a

Newspace 199.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(199))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
199.2.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{2} + 4q^{3} - q^{4} + 6q^{5} - 2q^{6} + O(q^{8})$	−	$+1$
199.2.a.b	4	degree 4	$4q - 3q^{2} - 2q^{3} + q^{4} - 5q^{5} - q^{6} - 3q^{7} + O(q^{8})$	+	$-1$
199.2.a.c	10	degree 10	$10q + 5q^{2} - 4q^{3} + 13q^{4} - q^{5} + 3q^{6} - 3q^{7} + O(q^{8})$	−	$+1$

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 $T$
199.2.a.a	$x^{2} - 3x + 1$
199.2.a.b	$x^{4} + 5x^{3} + 6x^{2} - 1$
199.2.a.c	$x^{10} - x^{9} - 46x^{8} + 45x^{7} + 684x^{6} - 768x^{5} - 3731x^{4} + 4604x^{3} + 5388x^{2} - 5538x - 1961$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(199))$	16
Old forms	0
Cusp forms $S_{2}(\Gamma_0(199))$	16
Eisenstein series $E_{2}(\Gamma_0(199))$	1
Modular forms $M_{2}(\Gamma_0(199))$	17

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, 199]: [0, 17] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 16 = 1 x 16 (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(199, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 199:2 1000

← 198.2.a · 200.2.a →