Base field 4.4.16225.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 13 x^2 + 6 x + 36\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29, 29, -\frac{1}{6} w^3 + \frac{1}{6} w^2 + \frac{13}{6} w]$ |
| Dimension: | $25$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $50$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{25} - 13 x^{24} + 22 x^{23} + 403 x^{22} - 1870 x^{21} - 3039 x^{20} + 33764 x^{19} - 25135 x^{18} - 264060 x^{17} + 527698 x^{16} + 886086 x^{15} - 3287837 x^{14} - 260574 x^{13} + 9588366 x^{12} - 5868290 x^{11} - 13393664 x^{10} + 14299113 x^9 + 7998182 x^8 - 12941264 x^7 - 1852036 x^6 + 5315462 x^5 + 197285 x^4 - 942660 x^3 - 52384 x^2 + 44736 x + 4864\) |
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 | $[29, 29, -\frac{1}{6} w^3 + \frac{1}{6} w^2 + \frac{13}{6} w]$ | $-1$ |
| 29 | $[29, 29, w - 1]$ | $...$ |
| 31 | $[31, 31, \frac{1}{3} w^3 - \frac{1}{3} w^2 - \frac{10}{3} w + 3]$ | $...$ |
| 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 |
|---|---|---|
| $29$ | $[29, 29, -\frac{1}{6} w^3 + \frac{1}{6} w^2 + \frac{13}{6} w]$ | $1$ |