Base field 5.5.89417.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} - x^{2} + 8x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[37, 37, -w^{3} + 4w - 1]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 8x^{11} + 11x^{10} + 63x^{9} - 193x^{8} + 3x^{7} + 466x^{6} - 225x^{5} - 449x^{4} + 203x^{3} + 206x^{2} - 35x - 28\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{2} - 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{4} - 5w^{2} + 4]$ | $-37e^{11} + 228e^{10} + 11e^{9} - 2304e^{8} + 2904e^{7} + 5163e^{6} - 7645e^{5} - 5628e^{4} + 6012e^{3} + 3499e^{2} - 1006e - 546$ |
| 11 | $[11, 11, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $-71e^{11} + 437e^{10} + 24e^{9} - 4420e^{8} + 5543e^{7} + 9937e^{6} - 14604e^{5} - 10880e^{4} + 11482e^{3} + 6768e^{2} - 1915e - 1056$ |
| 17 | $[17, 17, w^{4} - 4w^{2} + 2]$ | $-137e^{11} + 842e^{10} + 55e^{9} - 8535e^{8} + 10619e^{7} + 19332e^{6} - 28092e^{5} - 21344e^{4} + 22151e^{3} + 13314e^{2} - 3698e - 2086$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}115e^{11} - 704e^{10} - 65e^{9} + 7175e^{8} - 8748e^{7} - 16545e^{6} + 23396e^{5} + 18586e^{4} - 18602e^{3} - 11589e^{2} + 3114e + 1809$ |
| 37 | $[37, 37, -w^{4} + 2w^{3} + 5w^{2} - 7w - 5]$ | $-77e^{11} + 475e^{10} + 19e^{9} - 4790e^{8} + 6072e^{7} + 10663e^{6} - 15896e^{5} - 11578e^{4} + 12438e^{3} + 7223e^{2} - 2075e - 1134$ |
| 37 | $[37, 37, -w^{3} + 4w - 1]$ | $\phantom{-}1$ |
| 41 | $[41, 41, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}39e^{11} - 240e^{10} - 14e^{9} + 2431e^{8} - 3042e^{7} - 5489e^{6} + 8056e^{5} + 6014e^{4} - 6378e^{3} - 3719e^{2} + 1085e + 582$ |
| 41 | $[41, 41, -w^{3} + 2w + 2]$ | $\phantom{-}79e^{11} - 486e^{10} - 28e^{9} + 4917e^{8} - 6153e^{7} - 11068e^{6} + 16209e^{5} + 12156e^{4} - 12745e^{3} - 7591e^{2} + 2136e + 1194$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}208e^{11} - 1277e^{10} - 93e^{9} + 12965e^{8} - 16040e^{7} - 29524e^{6} + 42573e^{5} + 32785e^{4} - 33683e^{3} - 20464e^{2} + 5651e + 3208$ |
| 49 | $[49, 7, w^{4} - 5w^{2} + 2]$ | $-200e^{11} + 1227e^{10} + 95e^{9} - 12468e^{8} + 15374e^{7} + 28468e^{6} - 40877e^{5} - 31664e^{4} + 32358e^{3} + 19735e^{2} - 5415e - 3082$ |
| 53 | $[53, 53, w^{4} - w^{3} - 5w^{2} + 2w + 5]$ | $-218e^{11} + 1341e^{10} + 80e^{9} - 13580e^{8} + 16971e^{7} + 30653e^{6} - 44845e^{5} - 33681e^{4} + 35359e^{3} + 20963e^{2} - 5930e - 3282$ |
| 59 | $[59, 59, w^{4} - w^{3} - 4w^{2} + 3w - 1]$ | $-10e^{11} + 65e^{10} - 20e^{9} - 609e^{8} + 987e^{7} + 1000e^{6} - 2293e^{5} - 670e^{4} + 1630e^{3} + 381e^{2} - 278e - 60$ |
| 67 | $[67, 67, -w^{4} + 3w^{2} + 2w + 2]$ | $-39e^{11} + 238e^{10} + 27e^{9} - 2436e^{8} + 2924e^{7} + 5695e^{6} - 7896e^{5} - 6481e^{4} + 6340e^{3} + 4047e^{2} - 1082e - 636$ |
| 79 | $[79, 79, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}198e^{11} - 1217e^{10} - 79e^{9} + 12336e^{8} - 15353e^{7} - 27941e^{6} + 40623e^{5} + 30855e^{4} - 32069e^{3} - 19241e^{2} + 5382e + 3016$ |
| 81 | $[81, 3, -w^{4} + 6w^{2} + w - 8]$ | $-84e^{11} + 517e^{10} + 29e^{9} - 5232e^{8} + 6556e^{7} + 11781e^{6} - 17302e^{5} - 12899e^{4} + 13620e^{3} + 8009e^{2} - 2279e - 1242$ |
| 83 | $[83, 83, w^{4} + w^{3} - 5w^{2} - 4w + 1]$ | $-197e^{11} + 1213e^{10} + 64e^{9} - 12265e^{8} + 15404e^{7} + 27548e^{6} - 40559e^{5} - 30156e^{4} + 31880e^{3} + 18810e^{2} - 5330e - 2956$ |
| 89 | $[89, 89, -w^{4} + 5w^{2} + w - 1]$ | $-120e^{11} + 742e^{10} + 17e^{9} - 7454e^{8} + 9570e^{7} + 16377e^{6} - 24862e^{5} - 17540e^{4} + 19330e^{3} + 10919e^{2} - 3204e - 1702$ |
| 97 | $[97, 97, -w^{4} + 2w^{3} + 5w^{2} - 5w - 5]$ | $-127e^{11} + 778e^{10} + 68e^{9} - 7921e^{8} + 9692e^{7} + 18210e^{6} - 25859e^{5} - 20442e^{4} + 20548e^{3} + 12799e^{2} - 3456e - 2014$ |
| 101 | $[101, 101, 2w^{2} - w - 2]$ | $\phantom{-}67e^{11} - 411e^{10} - 32e^{9} + 4177e^{8} - 5152e^{7} - 9537e^{6} + 13722e^{5} + 10572e^{4} - 10885e^{3} - 6566e^{2} + 1841e + 1034$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37, 37, -w^{3} + 4w - 1]$ | $-1$ |