Base field 4.4.19225.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 15 x^2 + 2 x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29, 29, w + 1]$ |
| Dimension: | $25$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $67$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{25} - x^{24} - 52 x^{23} + 48 x^{22} + 1127 x^{21} - 944 x^{20} - 13374 x^{19} + 10054 x^{18} + 96286 x^{17} - 65326 x^{16} - 440550 x^{15} + 277639 x^{14} + 1304601 x^{13} - 802787 x^{12} - 2495942 x^{11} + 1588148 x^{10} + 3008007 x^9 - 2087291 x^8 - 2137888 x^7 + 1707881 x^6 + 757336 x^5 - 773466 x^4 - 60648 x^3 + 150180 x^2 - 19060 x - 3779\) |
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 | $[25, 5, w^3 - 3 w^2 - 7 w + 15]$ | $...$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}1$ |
| 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 | $[59, 59, 2 w^2 - w - 13]$ | $...$ |
| 59 | $[59, 59, \frac{9}{2} w^3 - \frac{31}{2} w^2 - \frac{61}{2} w + 85]$ | $...$ |
| 61 | $[61, 61, 2 w^3 - 6 w^2 - 15 w + 31]$ | $...$ |
| 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 | $[79, 79, -3 w^3 + 10 w^2 + 19 w - 51]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, w + 1]$ | $-1$ |