Base field 3.3.1901.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 9, w^{2} - 2w - 9]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - x^{6} - 11x^{5} + 9x^{4} + 29x^{3} - 9x^{2} - 19x - 3\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 4 | $[4, 2, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 5e^{4} + 5e^{3} + \frac{21}{2}e^{2} - \frac{15}{2}e - 4$ |
| 9 | $[9, 3, -w^{2} + 2w + 7]$ | $\phantom{-}\frac{1}{2}e^{6} - e^{5} - 5e^{4} + 9e^{3} + \frac{19}{2}e^{2} - 10e - 4$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{2}e^{4} - 3e^{2} - \frac{1}{2}$ |
| 13 | $[13, 13, -w + 3]$ | $-\frac{1}{2}e^{4} + 3e^{2} + \frac{1}{2}$ |
| 13 | $[13, 13, -w + 1]$ | $-\frac{1}{2}e^{5} + 5e^{3} - \frac{19}{2}e - 2$ |
| 17 | $[17, 17, -w^{2} - 2w + 1]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - \frac{11}{2}e^{4} + 4e^{3} + \frac{29}{2}e^{2} - \frac{5}{2}e - \frac{15}{2}$ |
| 23 | $[23, 23, w^{2} - 2w - 5]$ | $\phantom{-}\frac{3}{2}e^{6} - 2e^{5} - \frac{31}{2}e^{4} + 18e^{3} + \frac{67}{2}e^{2} - 20e - \frac{27}{2}$ |
| 31 | $[31, 31, 2w + 3]$ | $-\frac{1}{2}e^{6} + e^{5} + \frac{9}{2}e^{4} - 9e^{3} - \frac{13}{2}e^{2} + 10e + \frac{5}{2}$ |
| 31 | $[31, 31, -2w^{2} + 3w + 15]$ | $\phantom{-}e^{6} - e^{5} - 10e^{4} + 9e^{3} + 21e^{2} - 10e - 8$ |
| 31 | $[31, 31, 3w + 7]$ | $\phantom{-}\frac{1}{2}e^{6} - e^{5} - \frac{9}{2}e^{4} + 8e^{3} + \frac{9}{2}e^{2} - 5e + \frac{7}{2}$ |
| 37 | $[37, 37, 3w^{2} - 4w - 27]$ | $\phantom{-}\frac{1}{2}e^{6} - e^{5} - \frac{11}{2}e^{4} + 8e^{3} + \frac{25}{2}e^{2} - 5e - \frac{7}{2}$ |
| 41 | $[41, 41, -2w^{2} + 7w + 1]$ | $-e^{5} + \frac{1}{2}e^{4} + 9e^{3} - 5e^{2} - 14e + \frac{3}{2}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-e^{6} + e^{5} + 10e^{4} - 10e^{3} - 19e^{2} + 15e + 6$ |
| 61 | $[61, 61, 4w^{2} - 12w - 11]$ | $-\frac{3}{2}e^{4} + e^{3} + 11e^{2} - 9e - \frac{25}{2}$ |
| 71 | $[71, 71, w^{2} - 2w - 11]$ | $-\frac{1}{2}e^{6} + e^{5} + \frac{11}{2}e^{4} - 9e^{3} - \frac{25}{2}e^{2} + 14e + \frac{3}{2}$ |
| 97 | $[97, 97, 3w + 5]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - \frac{9}{2}e^{4} + 5e^{3} + \frac{17}{2}e^{2} - \frac{11}{2}e - \frac{17}{2}$ |
| 101 | $[101, 101, 2w^{2} - 6w - 7]$ | $\phantom{-}e^{6} - 3e^{5} - \frac{19}{2}e^{4} + 28e^{3} + 16e^{2} - 39e - \frac{21}{2}$ |
| 103 | $[103, 103, 2w^{2} - 3w - 19]$ | $-\frac{3}{2}e^{6} + e^{5} + \frac{27}{2}e^{4} - 10e^{3} - \frac{35}{2}e^{2} + 7e - \frac{13}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-1$ |