Atlas › Modular forms › Weight 2 › Level 193 › 193.2.a

Newspace 193.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(193))$

Newforms

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

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 $T$
193.2.a.a	$x^{2} + 5x + 5$
193.2.a.b	$x^{5} + 7x^{4} + 9x^{3} - x^{2} - 4x - 1$
193.2.a.c	$x^{8} - 7x^{7} + x^{6} + 80x^{5} - 117x^{4} - 214x^{3} + 457x^{2} - 30x - 169$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(193))$	15
Old forms	0
Cusp forms $S_{2}(\Gamma_0(193))$	15
Eisenstein series $E_{2}(\Gamma_0(193))$	1
Modular forms $M_{2}(\Gamma_0(193))$	16

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.166 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, 193]: [0, 16] (certified at ell = 2147483137)
T = [(2, 1), (3, 1)]; 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(193, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 193:2 1000

← 192.2.a · 194.2.a →