Base field 5.5.160801.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ |
| Dimension: | $54$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $94$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{54} - 8x^{53} - 78x^{52} + 762x^{51} + 2574x^{50} - 33826x^{49} - 42437x^{48} + 930782x^{47} + 181383x^{46} - 17815273x^{45} + 7785534x^{44} + 252333467x^{43} - 214915442x^{42} - 2747655917x^{41} + 3126556507x^{40} + 23594371035x^{39} - 31571588381x^{38} - 162653252461x^{37} + 239745949101x^{36} + 911831417639x^{35} - 1419358529402x^{34} - 4195810156032x^{33} + 6677736862417x^{32} + 15951848117206x^{31} - 25231369211201x^{30} - 50312842985146x^{29} + 76969398527966x^{28} + 131871335690701x^{27} - 189863893018278x^{26} - 286983431566165x^{25} + 378212943979605x^{24} + 516728095499067x^{23} - 606124977248242x^{22} - 764938176309047x^{21} + 776851222979380x^{20} + 922606933491288x^{19} - 789952008458111x^{18} - 896051700167801x^{17} + 630991564836487x^{16} + 690661880895221x^{15} - 391195021709935x^{14} - 415014470760050x^{13} + 185606840766621x^{12} + 190091237569015x^{11} - 66327626536037x^{10} - 64421394648291x^{9} + 17548830650021x^{8} + 15484972460617x^{7} - 3376019348673x^{6} - 2471755884255x^{5} + 460001481516x^{4} + 232739680064x^{3} - 41195698624x^{2} - 9716249600x + 1840286720\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $...$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $...$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $...$ |
| 17 | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $...$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 2]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $...$ |
| 31 | $[31, 31, w^{3} - 4w + 2]$ | $...$ |
| 32 | $[32, 2, 2]$ | $...$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $...$ |
| 53 | $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ | $...$ |
| 59 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $...$ |
| 61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $\phantom{-}1$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $...$ |
| 71 | $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ | $...$ |
| 79 | $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ | $...$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ | $...$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ | $...$ |
| 83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ | $...$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $61$ | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $-1$ |