Atlas › Modular forms › Weight 4 › Level 193 › 193.4.a

Newspace 193.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(193))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
193.4.a.a	23	degree 23	$23q - 10q^{2} - 26q^{3} + 78q^{4} - 60q^{5} - 34q^{6} - 82q^{7} + O(q^{8})$	−	$-1$
193.4.a.b	25	degree 25	$25q + 10q^{2} + 22q^{3} + 102q^{4} + 50q^{5} + 38q^{6} + 86q^{7} + O(q^{8})$	+	$+1$

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 $T$
193.4.a.a	$x^{23} + 36x^{22} + 148x^{21} - 8133x^{20} - 82535x^{19} + 608446x^{18} + 9655058x^{17} - 17048295x^{16} - 540193314x^{15} - 81092688x^{14} + 16913944389x^{13} + 16832883068x^{12} - 305492922700x^{11} - 449962571305x^{10} + 3027752565671x^{9} + 5921806891260x^{8} - 13628691327810x^{7} - 39915267687345x^{6} + 4001608637093x^{5} + 100838506017392x^{4} + 118113462130683x^{3} + 50711989117005x^{2} + 5641033152000x - 248677774125$
193.4.a.b	$x^{25} - 32x^{24} - 152x^{23} + 14307x^{22} - 61687x^{21} - 2543390x^{20} + 20512270x^{19} + 232597141x^{18} - 2605586242x^{17} - 11660950688x^{16} + 182086506497x^{15} + 303030190564x^{14} - 7730590822100x^{13} - 2648375596321x^{12} + 206307070504203x^{11} - 42008689848676x^{10} - 3457120130777422x^{9} + 822045288476995x^{8} + 34951127230743153x^{7} + 3412401749523912x^{6} - 188924899517238917x^{5} - 118757972954840027x^{4} + 372306833758587672x^{3} + 371847600483054299x^{2} - 75288552522086368x - 103745154310658704$

Orbit

Characteristic polynomial of

T

193.4.a.a

x^{23} + 36x^{22} + 148x^{21} - 8133x^{20} - 82535x^{19} + 608446x^{18} + 9655058x^{17} - 17048295x^{16} - 540193314x^{15} - 81092688x^{14} + 16913944389x^{13} + 16832883068x^{12} - 305492922700x^{11} - 449962571305x^{10} + 3027752565671x^{9} + 5921806891260x^{8} - 13628691327810x^{7} - 39915267687345x^{6} + 4001608637093x^{5} + 100838506017392x^{4} + 118113462130683x^{3} + 50711989117005x^{2} + 5641033152000x - 248677774125

193.4.a.b

x^{25} - 32x^{24} - 152x^{23} + 14307x^{22} - 61687x^{21} - 2543390x^{20} + 20512270x^{19} + 232597141x^{18} - 2605586242x^{17} - 11660950688x^{16} + 182086506497x^{15} + 303030190564x^{14} - 7730590822100x^{13} - 2648375596321x^{12} + 206307070504203x^{11} - 42008689848676x^{10} - 3457120130777422x^{9} + 822045288476995x^{8} + 34951127230743153x^{7} + 3412401749523912x^{6} - 188924899517238917x^{5} - 118757972954840027x^{4} + 372306833758587672x^{3} + 371847600483054299x^{2} - 75288552522086368x - 103745154310658704

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(193))$	48
Old forms	0
Cusp forms $S_{4}(\Gamma_0(193))$	48
Eisenstein series $E_{4}(\Gamma_0(193))$	2
Modular forms $M_{4}(\Gamma_0(193))$	50

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.138 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]: [1, 50] (certified at ell = 2147483137)
T = [(2, 1), (3, 1)]; h of degree 48 = 1 x 48 (phi(ord eps) x dim S_k^new); 7 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, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 193:4 1000

← 192.4.a · 194.4.a →