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: | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ |
| Dimension: | $52$ |
| 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:
| \(x^{52} - 7x^{51} - 85x^{50} + 686x^{49} + 3178x^{48} - 31193x^{47} - 66674x^{46} + 874799x^{45} + 784644x^{44} - 16967924x^{43} - 2706148x^{42} + 241973311x^{41} - 78598802x^{40} - 2633240276x^{39} + 1744074778x^{38} + 22406839831x^{37} - 20283591954x^{36} - 151580669265x^{35} + 163916718615x^{34} + 824628997119x^{33} - 994545481296x^{32} - 3635958948903x^{31} + 4680968575894x^{30} + 13058586620075x^{29} - 17358455489728x^{28} - 38301278260262x^{27} + 51050772471985x^{26} + 91762298429914x^{25} - 119130339509585x^{24} - 179132576699386x^{23} + 219557426921909x^{22} + 283254301663308x^{21} - 316413516720657x^{20} - 358967700363277x^{19} + 350802664693401x^{18} + 358332077160534x^{17} - 291884229954786x^{16} - 274211074477745x^{15} + 175645061436315x^{14} + 154227402184047x^{13} - 72337609769008x^{12} - 59634695111855x^{11} + 18816029242434x^{10} + 14176687262995x^{9} - 2821268569859x^{8} - 1699907258956x^{7} + 250752644061x^{6} + 79994904825x^{5} - 9146229328x^{4} - 1288499016x^{3} + 68559788x^{2} + 7843704x + 152944\) |
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 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $\phantom{-}1$ |
| 61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $...$ |
| 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 |
|---|---|---|
| $59$ | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $-1$ |