Base field 4.4.19225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ |
Dimension: | $24$ |
CM: | no |
Base change: | no |
Newspace dimension: | $63$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{24} + 5x^{23} - 45x^{22} - 248x^{21} + 780x^{20} + 4967x^{19} - 6627x^{18} - 52664x^{17} + 28503x^{16} + 325183x^{15} - 52616x^{14} - 1206004x^{13} - 915x^{12} + 2662580x^{11} + 64518x^{10} - 3347546x^{9} + 203900x^{8} + 2190065x^{7} - 511408x^{6} - 615426x^{5} + 265314x^{4} + 30024x^{3} - 34123x^{2} + 6398x - 372\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w + 2]$ | $\phantom{-}e$ |
4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ | $...$ |
9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ | $...$ |
9 | $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ | $...$ |
11 | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ | $...$ |
11 | $[11, 11, -w - 3]$ | $...$ |
25 | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ | $\phantom{-}1$ |
29 | $[29, 29, w + 1]$ | $...$ |
29 | $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ | $...$ |
31 | $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ | $...$ |
31 | $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ | $...$ |
31 | $[31, 31, -w + 3]$ | $...$ |
31 | $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ | $...$ |
59 | $[59, 59, 2w^{2} - w - 13]$ | $...$ |
59 | $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ | $...$ |
61 | $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ | $...$ |
61 | $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ | $...$ |
71 | $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ | $...$ |
71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ | $...$ |
79 | $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$25$ | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ | $-1$ |