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: | $40$ |
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:
\(x^{40} + 4x^{39} - 65x^{38} - 260x^{37} + 1931x^{36} + 7662x^{35} - 34856x^{34} - 135646x^{33} + 428682x^{32} + 1611347x^{31} - 3816172x^{30} - 13583622x^{29} + 25475314x^{28} + 83785299x^{27} - 130176442x^{26} - 384110564x^{25} + 514247587x^{24} + 1315591010x^{23} - 1572058032x^{22} - 3353921800x^{21} + 3691269990x^{20} + 6285373115x^{19} - 6549482227x^{18} - 8467065366x^{17} + 8552442071x^{16} + 7921655062x^{15} - 7906681634x^{14} - 4903826649x^{13} + 4903972120x^{12} + 1893428383x^{11} - 1905704130x^{10} - 435851043x^{9} + 432945888x^{8} + 58886438x^{7} - 53134561x^{6} - 4871147x^{5} + 3125988x^{4} + 277364x^{3} - 66647x^{2} - 8071x - 210\) |
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 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $-1$ |
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 |
---|---|---|
$61$ | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $1$ |