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: | $[7, 7, -8w - 63]$ |
| Dimension: | $39$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $71$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{39} - 60x^{37} + x^{36} + 1647x^{35} - 62x^{34} - 27421x^{33} + 1729x^{32} + 309508x^{31} - 28754x^{30} - 2507813x^{29} + 318596x^{28} + 15065938x^{27} - 2487782x^{26} - 68342543x^{25} + 14117770x^{24} + 236150024x^{23} - 59160744x^{22} - 622405682x^{21} + 184101151x^{20} + 1244483272x^{19} - 424150152x^{18} - 1864127846x^{17} + 715110286x^{16} + 2048437224x^{15} - 863505941x^{14} - 1599844770x^{13} + 721679509x^{12} + 848387480x^{11} - 396604813x^{10} - 286632302x^{9} + 133179414x^{8} + 56681139x^{7} - 24811209x^{6} - 5845467x^{5} + 2277465x^{4} + 273179x^{3} - 88691x^{2} - 4244x + 931\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 8]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w + 9]$ | $...$ |
| 5 | $[5, 5, -76w + 675]$ | $...$ |
| 5 | $[5, 5, 76w + 599]$ | $...$ |
| 7 | $[7, 7, -8w - 63]$ | $-1$ |
| 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 |
|---|---|---|
| $7$ | $[7, 7, -8w - 63]$ | $1$ |