Base field \(\Q(\sqrt{58}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 58\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11, 11, w + 5]$ |
| Dimension: | $39$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $156$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{39} - 11x^{38} + 3x^{37} + 387x^{36} - 1096x^{35} - 5393x^{34} + 26412x^{33} + 31362x^{32} - 320510x^{31} + 63274x^{30} + 2394931x^{29} - 2451712x^{28} - 11724499x^{27} + 20178096x^{26} + 37544996x^{25} - 96882602x^{24} - 71482387x^{23} + 309945970x^{22} + 40215407x^{21} - 685770818x^{20} + 180395747x^{19} + 1052465878x^{18} - 581373388x^{17} - 1099770297x^{16} + 876964944x^{15} + 753323588x^{14} - 789473366x^{13} - 319360910x^{12} + 440409288x^{11} + 77401389x^{10} - 152222284x^{9} - 8835360x^{8} + 31805017x^{7} - 2118x^{6} - 3802844x^{5} + 90570x^{4} + 233770x^{3} - 5507x^{2} - 5698x + 33\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $...$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 7 | $[7, 7, -2w + 15]$ | $...$ |
| 7 | $[7, 7, -2w - 15]$ | $...$ |
| 11 | $[11, 11, w + 5]$ | $-1$ |
| 11 | $[11, 11, w + 6]$ | $...$ |
| 19 | $[19, 19, w + 1]$ | $...$ |
| 19 | $[19, 19, w + 18]$ | $...$ |
| 23 | $[23, 23, w + 9]$ | $...$ |
| 23 | $[23, 23, -w + 9]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 29 | $[29, 29, w]$ | $...$ |
| 37 | $[37, 37, w + 13]$ | $...$ |
| 37 | $[37, 37, w + 24]$ | $...$ |
| 43 | $[43, 43, w + 12]$ | $...$ |
| 43 | $[43, 43, w + 31]$ | $...$ |
| 61 | $[61, 61, w + 27]$ | $...$ |
| 61 | $[61, 61, w + 34]$ | $...$ |
| 71 | $[71, 71, 12w - 91]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w + 5]$ | $1$ |