Base field \(\Q(\sqrt{67}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 67\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11,11,-6w - 49]$ |
| Dimension: | $48$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $96$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{48} - 11x^{47} - 10x^{46} + 530x^{45} - 1082x^{44} - 11002x^{43} + 40689x^{42} + 122803x^{41} - 720012x^{40} - 665094x^{39} + 8009544x^{38} - 1045943x^{37} - 61598518x^{36} + 50841485x^{35} + 341333496x^{34} - 475474761x^{33} - 1381747451x^{32} + 2724060571x^{31} + 4039948355x^{30} - 11035356689x^{29} - 8056511975x^{28} + 33168077849x^{27} + 8630068638x^{26} - 75372509944x^{25} + 4802052946x^{24} + 130137326752x^{23} - 39502892271x^{22} - 169997788098x^{21} + 83715422505x^{20} + 165986719668x^{19} - 108112812654x^{18} - 118674353139x^{17} + 94545552676x^{16} + 60200574027x^{15} - 56976719876x^{14} - 20640947407x^{13} + 23315895086x^{12} + 4411309447x^{11} - 6242641952x^{10} - 498042676x^{9} + 1027554344x^{8} + 16120780x^{7} - 94314406x^{6} + 983473x^{5} + 4198188x^{4} + 4143x^{3} - 74605x^{2} - 2392x + 191\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -27w + 221]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 8]$ | $...$ |
| 3 | $[3, 3, -w - 8]$ | $...$ |
| 7 | $[7, 7, -11w + 90]$ | $...$ |
| 7 | $[7, 7, -11w - 90]$ | $...$ |
| 11 | $[11, 11, 6w - 49]$ | $...$ |
| 11 | $[11, 11, 6w + 49]$ | $-1$ |
| 17 | $[17, 17, 4w + 33]$ | $...$ |
| 17 | $[17, 17, -4w + 33]$ | $...$ |
| 25 | $[25, 5, -5]$ | $...$ |
| 29 | $[29, 29, -70w + 573]$ | $...$ |
| 29 | $[29, 29, 151w - 1236]$ | $...$ |
| 31 | $[31, 31, -w - 6]$ | $...$ |
| 31 | $[31, 31, w - 6]$ | $...$ |
| 37 | $[37, 37, -21w - 172]$ | $...$ |
| 37 | $[37, 37, -21w + 172]$ | $...$ |
| 43 | $[43, 43, 2w - 15]$ | $...$ |
| 43 | $[43, 43, 2w + 15]$ | $...$ |
| 67 | $[67, 67, -w]$ | $...$ |
| 73 | $[73, 73, -3w - 26]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-6w - 49]$ | $1$ |