Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 12 x^2 + 13 x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29,29,-w^2 + 7]$ |
| Dimension: | $30$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{30} - x^{29} - 143 x^{28} + 148 x^{27} + 8832 x^{26} - 9491 x^{25} - 310365 x^{24} + 349143 x^{23} + 6882882 x^{22} - 8185313 x^{21} - 101055570 x^{20} + 128220926 x^{19} + 1003204381 x^{18} - 1369219262 x^{17} - 6760035880 x^{16} + 10011860208 x^{15} + 30576382323 x^{14} - 49789358243 x^{13} - 90012743698 x^{12} + 165319819619 x^{11} + 160889528180 x^{10} - 353573619968 x^9 - 145029815736 x^8 + 455361857584 x^7 + 16214610784 x^6 - 309436127424 x^5 + 57995756160 x^4 + 83546149632 x^3 - 17935225856 x^2 - 7362103296 x + 226039808\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^3 + 3 w^2 + 5 w - 15]$ | $...$ |
| 9 | $[9, 3, -w^3 + 8 w + 8]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 19 | $[19, 19, w + 1]$ | $...$ |
| 19 | $[19, 19, -w^2 + 6]$ | $...$ |
| 19 | $[19, 19, -w^2 + 2 w + 5]$ | $...$ |
| 19 | $[19, 19, -w + 2]$ | $...$ |
| 25 | $[25, 5, 2 w^2 - 2 w - 13]$ | $...$ |
| 29 | $[29, 29, -w^2 + 9]$ | $...$ |
| 29 | $[29, 29, -w^2 + 2 w + 6]$ | $...$ |
| 29 | $[29, 29, w^2 - 7]$ | $-1$ |
| 29 | $[29, 29, -w^2 + 2 w + 8]$ | $...$ |
| 31 | $[31, 31, -2 w^2 + w + 12]$ | $...$ |
| 31 | $[31, 31, 2 w^2 - 3 w - 11]$ | $...$ |
| 41 | $[41, 41, -w]$ | $...$ |
| 41 | $[41, 41, -w + 1]$ | $...$ |
| 49 | $[49, 7, w^3 + 2 w^2 - 10 w - 20]$ | $...$ |
| 49 | $[49, 7, w^3 - 5 w^2 - 3 w + 27]$ | $...$ |
| 61 | $[61, 61, 2 w^2 - 3 w - 14]$ | $...$ |
| 61 | $[61, 61, 2 w^2 - w - 15]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29,29,-w^2 + 7]$ | $1$ |