Base field 4.4.19821.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ |
| Dimension: | $39$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $67$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{39} - 4x^{38} - 79x^{37} + 320x^{36} + 2841x^{35} - 11646x^{34} - 61698x^{33} + 255573x^{32} + 905307x^{31} - 3779471x^{30} - 9516085x^{29} + 39872865x^{28} + 74139221x^{27} - 309906766x^{26} - 436894189x^{25} + 1807143093x^{24} + 1968872760x^{23} - 7977586401x^{22} - 6808301163x^{21} + 26717446965x^{20} + 17989383860x^{19} - 67638243467x^{18} - 35851700611x^{17} + 128286083919x^{16} + 52593715570x^{15} - 179680142751x^{14} - 54514754921x^{13} + 182015904176x^{12} + 37212352532x^{11} - 129418604618x^{10} - 14433657458x^{9} + 61719627624x^{8} + 1698861906x^{7} - 18339339780x^{6} + 738522959x^{5} + 2983220860x^{4} - 233244047x^{3} - 205924042x^{2} + 10538424x + 4501581\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ | $...$ |
| 9 | $[9, 3, w + 1]$ | $...$ |
| 13 | $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ | $...$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 17 | $[17, 17, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 5]$ | $...$ |
| 19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 5]$ | $...$ |
| 23 | $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 2]$ | $...$ |
| 25 | $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ | $-1$ |
| 25 | $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$ | $...$ |
| 29 | $[29, 29, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 4w - 3]$ | $...$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w]$ | $...$ |
| 37 | $[37, 37, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $...$ |
| 41 | $[41, 41, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 4]$ | $...$ |
| 43 | $[43, 43, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w]$ | $...$ |
| 47 | $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ | $...$ |
| 59 | $[59, 59, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 4]$ | $...$ |
| 59 | $[59, 59, \frac{4}{3}w^{3} - \frac{5}{3}w^{2} - 10w + 9]$ | $...$ |
| 67 | $[67, 67, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w]$ | $...$ |
| 71 | $[71, 71, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ | $1$ |