Atlas › Modular forms › Weight 4 › Level 191 › 191.4.a

Newspace 191.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(191))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
191.4.a.a	17	degree 17	$17q - 4q^{2} - 11q^{3} + 34q^{4} - 21q^{5} - 57q^{6} - 38q^{7} + O(q^{8})$	−	$-1$
191.4.a.b	30	degree 30	$30q + 4q^{2} + 13q^{3} + 138q^{4} + 19q^{5} + 39q^{6} + 46q^{7} + O(q^{8})$	+	$+1$

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 $T$
191.4.a.a	$x^{17} + 15x^{16} - 158x^{15} - 2710x^{14} + 9519x^{13} + 179446x^{12} - 317075x^{11} - 5319753x^{10} + 6391752x^{9} + 67448214x^{8} - 46023009x^{7} - 355056244x^{6} + 4763082x^{5} + 633857387x^{4} + 466098455x^{3} + 60334400x^{2} - 30721035x - 6717759$
191.4.a.b	$x^{30} - 17x^{29} - 677x^{28} + 12081x^{27} + 196387x^{26} - 3672939x^{25} - 33128579x^{24} + 638607781x^{23} + 3722592469x^{22} - 71183893175x^{21} - 301760899082x^{20} + 5375862098123x^{19} + 18446323821259x^{18} - 282241284086102x^{17} - 859605186899258x^{16} + 10374358478803487x^{15} + 29991639103380332x^{14} - 265120659806949770x^{13} - 755588327075005241x^{12} + 4623767774844119475x^{11} + 13132808221806275813x^{10} - 53499525234274807255x^{9} - 149290325876158790535x^{8} + 396732181834367611214x^{7} + 1038620318497592468294x^{6} - 1817575956678153469068x^{5} - 4027169894902049891999x^{4} + 4825904052887599232793x^{3} + 7174141031095876094093x^{2} - 5958073443800316127100x - 2854520840695076990389$

Orbit

Characteristic polynomial of

T

191.4.a.a

x^{17} + 15x^{16} - 158x^{15} - 2710x^{14} + 9519x^{13} + 179446x^{12} - 317075x^{11} - 5319753x^{10} + 6391752x^{9} + 67448214x^{8} - 46023009x^{7} - 355056244x^{6} + 4763082x^{5} + 633857387x^{4} + 466098455x^{3} + 60334400x^{2} - 30721035x - 6717759

191.4.a.b

x^{30} - 17x^{29} - 677x^{28} + 12081x^{27} + 196387x^{26} - 3672939x^{25} - 33128579x^{24} + 638607781x^{23} + 3722592469x^{22} - 71183893175x^{21} - 301760899082x^{20} + 5375862098123x^{19} + 18446323821259x^{18} - 282241284086102x^{17} - 859605186899258x^{16} + 10374358478803487x^{15} + 29991639103380332x^{14} - 265120659806949770x^{13} - 755588327075005241x^{12} + 4623767774844119475x^{11} + 13132808221806275813x^{10} - 53499525234274807255x^{9} - 149290325876158790535x^{8} + 396732181834367611214x^{7} + 1038620318497592468294x^{6} - 1817575956678153469068x^{5} - 4027169894902049891999x^{4} + 4825904052887599232793x^{3} + 7174141031095876094093x^{2} - 5958073443800316127100x - 2854520840695076990389

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(191))$	47
Old forms	0
Cusp forms $S_{4}(\Gamma_0(191))$	47
Eisenstein series $E_{4}(\Gamma_0(191))$	2
Modular forms $M_{4}(\Gamma_0(191))$	49

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.134 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, 191]: [1, 49] (certified at ell = 2147483171)
T = [(2, 1), (3, 1)]; h of degree 47 = 1 x 47 (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(191, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 191:4 1000

← 190.4.a · 192.4.a →