Base field 3.3.1300.1
Generator \(w\), with minimal polynomial \(x^{3} - 10x - 10\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, -w^{2} + w + 7]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 3x^{11} - 12x^{10} - 40x^{9} + 47x^{8} + 195x^{7} - 54x^{6} - 425x^{5} - 54x^{4} + 400x^{3} + 124x^{2} - 130x - 50\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + 2w + 5]$ | $\phantom{-}\frac{2}{5}e^{11} + \frac{6}{5}e^{10} - \frac{19}{5}e^{9} - 13e^{8} + \frac{49}{5}e^{7} + 47e^{6} - \frac{8}{5}e^{5} - 67e^{4} - \frac{73}{5}e^{3} + 34e^{2} + \frac{38}{5}e - 2$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e^{11} + 2e^{10} - 12e^{9} - 22e^{8} + 51e^{7} + 82e^{6} - 95e^{5} - 123e^{4} + 77e^{3} + 68e^{2} - 22e - 10$ |
| 11 | $[11, 11, -2w^{2} + 5w + 9]$ | $-\frac{7}{5}e^{11} - \frac{16}{5}e^{10} + \frac{74}{5}e^{9} + 33e^{8} - \frac{254}{5}e^{7} - 111e^{6} + \frac{328}{5}e^{5} + 145e^{4} - \frac{142}{5}e^{3} - 78e^{2} + \frac{2}{5}e + 15$ |
| 13 | $[13, 13, -w^{2} + w + 7]$ | $-1$ |
| 13 | $[13, 13, w - 3]$ | $\phantom{-}\frac{4}{5}e^{11} - \frac{3}{5}e^{10} - \frac{88}{5}e^{9} - e^{8} + \frac{613}{5}e^{7} + 51e^{6} - \frac{1716}{5}e^{5} - 194e^{4} + \frac{1894}{5}e^{3} + 216e^{2} - \frac{694}{5}e - 71$ |
| 17 | $[17, 17, -w^{2} + 2w + 7]$ | $-\frac{7}{5}e^{11} - \frac{21}{5}e^{10} + \frac{69}{5}e^{9} + 45e^{8} - \frac{214}{5}e^{7} - 160e^{6} + \frac{258}{5}e^{5} + 224e^{4} - \frac{192}{5}e^{3} - 118e^{2} + \frac{92}{5}e + 14$ |
| 17 | $[17, 17, -2w^{2} + 5w + 7]$ | $-\frac{3}{5}e^{11} + \frac{6}{5}e^{10} + \frac{76}{5}e^{9} - 6e^{8} - \frac{556}{5}e^{7} - 22e^{6} + \frac{1567}{5}e^{5} + 139e^{4} - \frac{1683}{5}e^{3} - 164e^{2} + \frac{598}{5}e + 50$ |
| 17 | $[17, 17, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{9}{5}e^{11} + \frac{22}{5}e^{10} - \frac{98}{5}e^{9} - 47e^{8} + \frac{368}{5}e^{7} + 168e^{6} - \frac{626}{5}e^{5} - 244e^{4} + \frac{574}{5}e^{3} + 148e^{2} - \frac{224}{5}e - 29$ |
| 19 | $[19, 19, -w + 1]$ | $-\frac{7}{5}e^{11} - \frac{21}{5}e^{10} + \frac{64}{5}e^{9} + 44e^{8} - \frac{154}{5}e^{7} - 151e^{6} + \frac{13}{5}e^{5} + 199e^{4} + \frac{203}{5}e^{3} - 94e^{2} - \frac{108}{5}e + 8$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}\frac{1}{5}e^{11} + \frac{3}{5}e^{10} - \frac{7}{5}e^{9} - 6e^{8} - \frac{8}{5}e^{7} + 18e^{6} + \frac{146}{5}e^{5} - 11e^{4} - \frac{324}{5}e^{3} - 22e^{2} + \frac{194}{5}e + 17$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $-e^{11} - e^{10} + 15e^{9} + 13e^{8} - 82e^{7} - 61e^{6} + 199e^{5} + 123e^{4} - 207e^{3} - 98e^{2} + 72e + 24$ |
| 37 | $[37, 37, w^{2} - 7]$ | $\phantom{-}\frac{4}{5}e^{11} + \frac{12}{5}e^{10} - \frac{33}{5}e^{9} - 23e^{8} + \frac{58}{5}e^{7} + 67e^{6} + \frac{54}{5}e^{5} - 67e^{4} - \frac{111}{5}e^{3} + 34e^{2} + \frac{16}{5}e - 11$ |
| 41 | $[41, 41, w^{2} - w - 11]$ | $-\frac{1}{5}e^{11} + \frac{7}{5}e^{10} + \frac{42}{5}e^{9} - 11e^{8} - \frac{357}{5}e^{7} + 15e^{6} + \frac{1084}{5}e^{5} + 35e^{4} - \frac{1211}{5}e^{3} - 58e^{2} + \frac{406}{5}e + 19$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}2e^{11} + 3e^{10} - 27e^{9} - 35e^{8} + 134e^{7} + 145e^{6} - 304e^{5} - 264e^{4} + 312e^{3} + 212e^{2} - 112e - 62$ |
| 49 | $[49, 7, w^{2} - 3w - 1]$ | $-2e^{11} - 3e^{10} + 30e^{9} + 41e^{8} - 167e^{7} - 205e^{6} + 424e^{5} + 451e^{4} - 481e^{3} - 410e^{2} + 194e + 119$ |
| 59 | $[59, 59, w^{2} - 4w + 1]$ | $-\frac{12}{5}e^{11} - \frac{41}{5}e^{10} + \frac{104}{5}e^{9} + 87e^{8} - \frac{214}{5}e^{7} - 304e^{6} - \frac{102}{5}e^{5} + 414e^{4} + \frac{423}{5}e^{3} - 212e^{2} - \frac{168}{5}e + 21$ |
| 67 | $[67, 67, w^{2} - 3w - 7]$ | $\phantom{-}\frac{1}{5}e^{11} + \frac{18}{5}e^{10} + \frac{23}{5}e^{9} - 38e^{8} - \frac{303}{5}e^{7} + 129e^{6} + \frac{1046}{5}e^{5} - 159e^{4} - \frac{1244}{5}e^{3} + 56e^{2} + \frac{454}{5}e + 7$ |
| 71 | $[71, 71, 4w + 9]$ | $-\frac{9}{5}e^{11} - \frac{12}{5}e^{10} + \frac{133}{5}e^{9} + 31e^{8} - \frac{718}{5}e^{7} - 142e^{6} + \frac{1721}{5}e^{5} + 272e^{4} - \frac{1769}{5}e^{3} - 196e^{2} + \frac{644}{5}e + 43$ |
| 73 | $[73, 73, -4w^{2} + 8w + 23]$ | $\phantom{-}\frac{7}{5}e^{11} + \frac{31}{5}e^{10} - \frac{34}{5}e^{9} - 62e^{8} - \frac{156}{5}e^{7} + 192e^{6} + \frac{1022}{5}e^{5} - 194e^{4} - \frac{1498}{5}e^{3} + 30e^{2} + \frac{658}{5}e + 22$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{2} + w + 7]$ | $1$ |