Base field 4.4.16225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 6x + 36\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ |
Dimension: | $29$ |
CM: | no |
Base change: | no |
Newspace dimension: | $58$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{29} - 11x^{28} - 13x^{27} + 551x^{26} - 1076x^{25} - 10842x^{24} + 38885x^{23} + 101273x^{22} - 586763x^{21} - 337609x^{20} + 4987239x^{19} - 1939705x^{18} - 25939472x^{17} + 25826110x^{16} + 83969450x^{15} - 125447376x^{14} - 163367084x^{13} + 339966020x^{12} + 165724359x^{11} - 544879197x^{10} - 30858824x^{9} + 501139116x^{8} - 96471233x^{7} - 236683523x^{6} + 78154632x^{5} + 44339744x^{4} - 15574596x^{3} - 3051164x^{2} + 796672x + 22912\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ | $...$ |
4 | $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ | $\phantom{-}e$ |
9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ | $...$ |
9 | $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ | $...$ |
11 | $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ | $...$ |
19 | $[19, 19, w + 1]$ | $...$ |
19 | $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ | $...$ |
25 | $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ | $...$ |
29 | $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ | $...$ |
29 | $[29, 29, w - 1]$ | $...$ |
31 | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ | $-1$ |
31 | $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ | $...$ |
41 | $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ | $...$ |
41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ | $...$ |
59 | $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ | $...$ |
59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ | $...$ |
59 | $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ | $...$ |
79 | $[79, 79, w^{2} - 11]$ | $...$ |
79 | $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ | $...$ |
89 | $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ | $1$ |