Base field 4.4.18688.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ |
| Dimension: | $38$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $80$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{38} + 5x^{37} - 40x^{36} - 232x^{35} + 676x^{34} + 4878x^{33} - 5937x^{32} - 61521x^{31} + 22491x^{30} + 519237x^{29} + 78111x^{28} - 3098037x^{27} - 1555028x^{26} + 13456886x^{25} + 10277918x^{24} - 43170680x^{23} - 42120884x^{22} + 102651062x^{21} + 119447820x^{20} - 179783766x^{19} - 242725953x^{18} + 227844889x^{17} + 356251142x^{16} - 201642098x^{15} - 374582895x^{14} + 115798915x^{13} + 275773075x^{12} - 35298481x^{11} - 136365081x^{10} + 113643x^{9} + 42162099x^{8} + 3482269x^{7} - 7164695x^{6} - 854995x^{5} + 520097x^{4} + 37689x^{3} - 13471x^{2} + 235x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ | $...$ |
| 7 | $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ | $...$ |
| 9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ | $...$ |
| 9 | $[9, 3, w + 1]$ | $...$ |
| 17 | $[17, 17, w + 3]$ | $...$ |
| 17 | $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ | $...$ |
| 31 | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ | $\phantom{-}1$ |
| 31 | $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ | $...$ |
| 41 | $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ | $...$ |
| 41 | $[41, 41, w^{2} - 5]$ | $...$ |
| 41 | $[41, 41, 2w + 3]$ | $...$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ | $...$ |
| 47 | $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ | $...$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ | $...$ |
| 49 | $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ | $...$ |
| 73 | $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ | $...$ |
| 73 | $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ | $...$ |
| 73 | $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ | $...$ |
| 103 | $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ | $-1$ |