Base field \(\Q(\sqrt{389}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 97\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, -w - 9]$ |
| 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:
| \(x^{39} + 5x^{38} - 80x^{37} - 419x^{36} + 2871x^{35} + 15915x^{34} - 61100x^{33} - 363476x^{32} + 857579x^{31} + 5581864x^{30} - 8330082x^{29} - 61050807x^{28} + 56847253x^{27} + 491266139x^{26} - 267299288x^{25} - 2961718099x^{24} + 785471229x^{23} + 13491176814x^{22} - 777682529x^{21} - 46471010318x^{20} - 4681649723x^{19} + 120292892167x^{18} + 26937369518x^{17} - 230867704662x^{16} - 74055134679x^{15} + 321439953288x^{14} + 127377483784x^{13} - 314555178702x^{12} - 142110912570x^{11} + 207101760975x^{10} + 100253165117x^{9} - 86544875465x^{8} - 41757392443x^{7} + 21248505692x^{6} + 8875786914x^{5} - 2829003849x^{4} - 636023362x^{3} + 203225129x^{2} - 9030090x - 202703\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -3w - 28]$ | $...$ |
| 5 | $[5, 5, -3w + 31]$ | $...$ |
| 7 | $[7, 7, -w - 9]$ | $-1$ |
| 7 | $[7, 7, -w + 10]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, -2w - 19]$ | $...$ |
| 11 | $[11, 11, 2w - 21]$ | $...$ |
| 13 | $[13, 13, w - 11]$ | $...$ |
| 13 | $[13, 13, -w - 10]$ | $...$ |
| 17 | $[17, 17, -8w - 75]$ | $...$ |
| 17 | $[17, 17, -8w + 83]$ | $...$ |
| 19 | $[19, 19, -5w + 52]$ | $...$ |
| 19 | $[19, 19, 5w + 47]$ | $...$ |
| 41 | $[41, 41, -w - 7]$ | $...$ |
| 41 | $[41, 41, w - 8]$ | $...$ |
| 59 | $[59, 59, -w - 12]$ | $...$ |
| 59 | $[59, 59, w - 13]$ | $...$ |
| 67 | $[67, 67, -w - 5]$ | $...$ |
| 67 | $[67, 67, w - 6]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w - 9]$ | $1$ |