Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[31,31,-2w^{2} + 3w + 11]$ |
| Dimension: | $33$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $59$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{33} - 14x^{32} - 81x^{31} + 1973x^{30} - 637x^{29} - 116866x^{28} + 313439x^{27} + 3761516x^{26} - 16528202x^{25} - 69577575x^{24} + 454590453x^{23} + 661153716x^{22} - 7733535779x^{21} - 175319215x^{20} + 85663905890x^{19} - 77230371437x^{18} - 620521532016x^{17} + 1015547163823x^{16} + 2826119182089x^{15} - 6857289879369x^{14} - 7065850709040x^{13} + 27261526134530x^{12} + 4123593429018x^{11} - 62635914256836x^{10} + 23660591791338x^{9} + 73472868519262x^{8} - 54443637858924x^{7} - 30646182875952x^{6} + 33343730036440x^{5} + 1404674931980x^{4} - 5319225952360x^{3} + 292439972480x^{2} + 247333072992x - 15579258048\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ | $...$ |
| 9 | $[9, 3, -w^{3} + 8w + 8]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 19 | $[19, 19, w + 1]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $...$ |
| 19 | $[19, 19, -w + 2]$ | $...$ |
| 25 | $[25, 5, 2w^{2} - 2w - 13]$ | $...$ |
| 29 | $[29, 29, -w^{2} + 9]$ | $...$ |
| 29 | $[29, 29, -w^{2} + 2w + 6]$ | $...$ |
| 29 | $[29, 29, w^{2} - 7]$ | $...$ |
| 29 | $[29, 29, -w^{2} + 2w + 8]$ | $...$ |
| 31 | $[31, 31, -2w^{2} + w + 12]$ | $...$ |
| 31 | $[31, 31, 2w^{2} - 3w - 11]$ | $-1$ |
| 41 | $[41, 41, -w]$ | $...$ |
| 41 | $[41, 41, -w + 1]$ | $...$ |
| 49 | $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ | $...$ |
| 49 | $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ | $...$ |
| 61 | $[61, 61, 2w^{2} - 3w - 14]$ | $...$ |
| 61 | $[61, 61, 2w^{2} - w - 15]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31,31,-2w^{2} + 3w + 11]$ | $1$ |