Base field \(\Q(\sqrt{281}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 70\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5, 5, -76w + 675]$ |
| Dimension: | $30$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{30} - 3x^{29} - 42x^{28} + 124x^{27} + 789x^{26} - 2271x^{25} - 8767x^{24} + 24309x^{23} + 64138x^{22} - 168871x^{21} - 324919x^{20} + 799352x^{19} + 1164675x^{18} - 2634636x^{17} - 2957939x^{16} + 6076970x^{15} + 5229409x^{14} - 9738910x^{13} - 6175576x^{12} + 10650515x^{11} + 4489582x^{10} - 7702026x^{9} - 1648349x^{8} + 3473098x^{7} + 54017x^{6} - 857468x^{5} + 140702x^{4} + 77996x^{3} - 27015x^{2} + 2458x - 55\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 8]$ | $...$ |
| 2 | $[2, 2, -w + 9]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -76w + 675]$ | $-1$ |
| 5 | $[5, 5, 76w + 599]$ | $...$ |
| 7 | $[7, 7, -8w - 63]$ | $...$ |
| 7 | $[7, 7, -8w + 71]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 17 | $[17, 17, 42w + 331]$ | $...$ |
| 17 | $[17, 17, 42w - 373]$ | $...$ |
| 29 | $[29, 29, -6w - 47]$ | $...$ |
| 29 | $[29, 29, 6w - 53]$ | $...$ |
| 31 | $[31, 31, 10w + 79]$ | $...$ |
| 31 | $[31, 31, -10w + 89]$ | $...$ |
| 43 | $[43, 43, 2w - 19]$ | $...$ |
| 43 | $[43, 43, -2w - 17]$ | $...$ |
| 53 | $[53, 53, 194w + 1529]$ | $...$ |
| 53 | $[53, 53, -194w + 1723]$ | $...$ |
| 59 | $[59, 59, -110w - 867]$ | $...$ |
| 59 | $[59, 59, 110w - 977]$ | $...$ |
| 79 | $[79, 79, 650w - 5773]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -76w + 675]$ | $1$ |