Base field 6.6.1081856.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 7x^{2} + 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[31, 31, w^{5} - 6w^{3} - w^{2} + 5w]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 7x^{7} - 12x^{6} - 192x^{5} - 420x^{4} - 44x^{3} + 356x^{2} - 144x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - w^{3} - 4w^{2} + w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 5w]$ | $\phantom{-}\frac{7}{4}e^{7} + 13e^{6} - \frac{63}{4}e^{5} - 344e^{4} - 875e^{3} - 415e^{2} + 472e - 72$ |
| 17 | $[17, 17, -w^{2} + w + 2]$ | $-e^{7} - \frac{15}{2}e^{6} + \frac{17}{2}e^{5} + \frac{395}{2}e^{4} + \frac{1027}{2}e^{3} + 265e^{2} - 262e + 32$ |
| 23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 4w - 1]$ | $\phantom{-}\frac{23}{4}e^{7} + \frac{171}{4}e^{6} - 52e^{5} - 1133e^{4} - \frac{5743}{2}e^{3} - 1312e^{2} + 1623e - 260$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 4w]$ | $\phantom{-}\frac{11}{4}e^{7} + \frac{81}{4}e^{6} - 26e^{5} - 539e^{4} - 1343e^{3} - 563e^{2} + 814e - 142$ |
| 31 | $[31, 31, -w^{3} + 4w + 1]$ | $-\frac{15}{4}e^{7} - \frac{109}{4}e^{6} + \frac{73}{2}e^{5} + 725e^{4} + \frac{3593}{2}e^{3} + 786e^{2} - 1019e + 168$ |
| 31 | $[31, 31, w^{5} - 6w^{3} - w^{2} + 5w]$ | $-1$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 5w^{3} - 2w^{2} - 6w - 1]$ | $\phantom{-}\frac{3}{4}e^{7} + \frac{23}{4}e^{6} - \frac{13}{2}e^{5} - 154e^{4} - 387e^{3} - 123e^{2} + 305e - 68$ |
| 47 | $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ | $\phantom{-}\frac{1}{4}e^{7} + \frac{7}{4}e^{6} - 3e^{5} - 48e^{4} - 105e^{3} - 12e^{2} + 91e - 20$ |
| 49 | $[49, 7, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 3]$ | $\phantom{-}e^{7} + \frac{15}{2}e^{6} - \frac{19}{2}e^{5} - \frac{403}{2}e^{4} - \frac{983}{2}e^{3} - 147e^{2} + 374e - 78$ |
| 71 | $[71, 71, -w^{4} + 5w^{2} + w - 3]$ | $\phantom{-}\frac{27}{4}e^{7} + \frac{195}{4}e^{6} - \frac{135}{2}e^{5} - 1300e^{4} - 3184e^{3} - 1331e^{2} + 1843e - 314$ |
| 71 | $[71, 71, w^{4} - 5w^{2} - 2w + 4]$ | $-\frac{5}{4}e^{7} - \frac{37}{4}e^{6} + \frac{23}{2}e^{5} + 245e^{4} + 618e^{3} + 289e^{2} - 331e + 46$ |
| 73 | $[73, 73, -2w^{5} + w^{4} + 10w^{3} - 9w - 1]$ | $-\frac{15}{2}e^{7} - 55e^{6} + \frac{143}{2}e^{5} + 1463e^{4} + 3641e^{3} + 1568e^{2} - 2120e + 360$ |
| 73 | $[73, 73, -w^{5} + 6w^{3} + 2w^{2} - 5w - 1]$ | $-\frac{43}{4}e^{7} - \frac{315}{4}e^{6} + \frac{205}{2}e^{5} + 2093e^{4} + 5215e^{3} + 2296e^{2} - 2957e + 492$ |
| 79 | $[79, 79, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $\phantom{-}\frac{27}{4}e^{7} + \frac{195}{4}e^{6} - \frac{135}{2}e^{5} - 1300e^{4} - 3184e^{3} - 1331e^{2} + 1845e - 314$ |
| 89 | $[89, 89, w^{5} - 7w^{3} - w^{2} + 9w]$ | $-\frac{7}{4}e^{7} - \frac{49}{4}e^{6} + \frac{39}{2}e^{5} + 330e^{4} + \frac{1539}{2}e^{3} + 256e^{2} - 497e + 100$ |
| 97 | $[97, 97, 2w^{5} - 2w^{4} - 10w^{3} + 5w^{2} + 10w - 1]$ | $-\frac{41}{4}e^{7} - \frac{305}{4}e^{6} + \frac{185}{2}e^{5} + 2021e^{4} + 5125e^{3} + 2335e^{2} - 2917e + 472$ |
| 103 | $[103, 103, w^{5} - w^{4} - 4w^{3} + w^{2} + 3w + 2]$ | $-\frac{17}{4}e^{7} - \frac{125}{4}e^{6} + \frac{81}{2}e^{5} + 833e^{4} + 2067e^{3} + 839e^{2} - 1279e + 234$ |
| 103 | $[103, 103, -2w^{5} + w^{4} + 11w^{3} - w^{2} - 11w - 1]$ | $-\frac{9}{2}e^{7} - 33e^{6} + \frac{85}{2}e^{5} + 876e^{4} + 2193e^{3} + 992e^{2} - 1213e + 202$ |
| 103 | $[103, 103, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $-6e^{7} - 44e^{6} + \frac{113}{2}e^{5} + 1168e^{4} + \frac{5857}{2}e^{3} + 1327e^{2} - 1634e + 268$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, w^{5} - 6w^{3} - w^{2} + 5w]$ | $1$ |