Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 12 x^2 + 13 x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[31,31,-2 w^2 + 3 w + 11]$ |
| 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:
| \(x^{33} - 14 x^{32} - 81 x^{31} + 1973 x^{30} - 637 x^{29} - 116866 x^{28} + 313439 x^{27} + 3761516 x^{26} - 16528202 x^{25} - 69577575 x^{24} + 454590453 x^{23} + 661153716 x^{22} - 7733535779 x^{21} - 175319215 x^{20} + 85663905890 x^{19} - 77230371437 x^{18} - 620521532016 x^{17} + 1015547163823 x^{16} + 2826119182089 x^{15} - 6857289879369 x^{14} - 7065850709040 x^{13} + 27261526134530 x^{12} + 4123593429018 x^{11} - 62635914256836 x^{10} + 23660591791338 x^9 + 73472868519262 x^8 - 54443637858924 x^7 - 30646182875952 x^6 + 33343730036440 x^5 + 1404674931980 x^4 - 5319225952360 x^3 + 292439972480 x^2 + 247333072992 x - 15579258048\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^3 + 3 w^2 + 5 w - 15]$ | $...$ |
| 9 | $[9, 3, -w^3 + 8 w + 8]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 19 | $[19, 19, w + 1]$ | $...$ |
| 19 | $[19, 19, -w^2 + 6]$ | $...$ |
| 19 | $[19, 19, -w^2 + 2 w + 5]$ | $...$ |
| 19 | $[19, 19, -w + 2]$ | $...$ |
| 25 | $[25, 5, 2 w^2 - 2 w - 13]$ | $...$ |
| 29 | $[29, 29, -w^2 + 9]$ | $...$ |
| 29 | $[29, 29, -w^2 + 2 w + 6]$ | $...$ |
| 29 | $[29, 29, w^2 - 7]$ | $...$ |
| 29 | $[29, 29, -w^2 + 2 w + 8]$ | $...$ |
| 31 | $[31, 31, -2 w^2 + w + 12]$ | $...$ |
| 31 | $[31, 31, 2 w^2 - 3 w - 11]$ | $-1$ |
| 41 | $[41, 41, -w]$ | $...$ |
| 41 | $[41, 41, -w + 1]$ | $...$ |
| 49 | $[49, 7, w^3 + 2 w^2 - 10 w - 20]$ | $...$ |
| 49 | $[49, 7, w^3 - 5 w^2 - 3 w + 27]$ | $...$ |
| 61 | $[61, 61, 2 w^2 - 3 w - 14]$ | $...$ |
| 61 | $[61, 61, 2 w^2 - w - 15]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31,31,-2 w^2 + 3 w + 11]$ | $1$ |