Base field 3.3.1492.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, -2w^{2} + 3w + 16]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + x^{8} - 11x^{7} - 9x^{6} + 39x^{5} + 26x^{4} - 45x^{3} - 26x^{2} + 6x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{1}{2}e^{7} - \frac{9}{4}e^{6} - \frac{9}{2}e^{5} + \frac{25}{4}e^{4} + \frac{51}{4}e^{3} - \frac{11}{2}e^{2} - 11e - \frac{1}{2}$ |
| 7 | $[7, 7, w^{2} - 2w - 8]$ | $-\frac{3}{4}e^{8} - \frac{1}{2}e^{7} + \frac{31}{4}e^{6} + \frac{7}{2}e^{5} - \frac{103}{4}e^{4} - \frac{33}{4}e^{3} + \frac{55}{2}e^{2} + 10e - \frac{5}{2}$ |
| 7 | $[7, 7, -2w^{2} + 3w + 16]$ | $-1$ |
| 7 | $[7, 7, -w^{2} + 2w + 6]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{1}{2}e^{7} - \frac{9}{4}e^{6} - \frac{7}{2}e^{5} + \frac{29}{4}e^{4} + \frac{23}{4}e^{3} - \frac{19}{2}e^{2} + \frac{3}{2}$ |
| 11 | $[11, 11, w^{2} - 2w - 2]$ | $-\frac{1}{4}e^{8} - \frac{1}{2}e^{7} + \frac{13}{4}e^{6} + \frac{9}{2}e^{5} - \frac{57}{4}e^{4} - \frac{47}{4}e^{3} + \frac{43}{2}e^{2} + 8e - \frac{11}{2}$ |
| 19 | $[19, 19, -w + 2]$ | $\phantom{-}\frac{1}{4}e^{8} - \frac{1}{2}e^{7} - \frac{17}{4}e^{6} + \frac{7}{2}e^{5} + \frac{81}{4}e^{4} - \frac{17}{4}e^{3} - \frac{59}{2}e^{2} - 6e + \frac{11}{2}$ |
| 23 | $[23, 23, -w^{2} + 3w + 1]$ | $-\frac{1}{4}e^{8} - \frac{1}{2}e^{7} + \frac{9}{4}e^{6} + \frac{9}{2}e^{5} - \frac{25}{4}e^{4} - \frac{47}{4}e^{3} + \frac{11}{2}e^{2} + 8e + \frac{1}{2}$ |
| 25 | $[25, 5, w^{2} - w - 9]$ | $-\frac{3}{2}e^{8} - e^{7} + \frac{33}{2}e^{6} + 8e^{5} - \frac{113}{2}e^{4} - \frac{39}{2}e^{3} + 58e^{2} + 17e - 7$ |
| 27 | $[27, 3, 3]$ | $-\frac{3}{4}e^{8} - \frac{1}{2}e^{7} + \frac{31}{4}e^{6} + \frac{5}{2}e^{5} - \frac{103}{4}e^{4} + \frac{3}{4}e^{3} + \frac{59}{2}e^{2} - 10e - \frac{17}{2}$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $\phantom{-}\frac{3}{4}e^{8} - \frac{1}{2}e^{7} - \frac{39}{4}e^{6} + \frac{9}{2}e^{5} + \frac{155}{4}e^{4} - \frac{47}{4}e^{3} - \frac{99}{2}e^{2} + 5e + \frac{25}{2}$ |
| 29 | $[29, 29, w^{2} - 2w - 4]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{15}{2}e^{6} - 3e^{5} + \frac{65}{2}e^{4} + \frac{35}{2}e^{3} - 42e^{2} - 21e + 1$ |
| 29 | $[29, 29, -w^{2} + w + 11]$ | $\phantom{-}\frac{3}{2}e^{8} + 2e^{7} - \frac{29}{2}e^{6} - 14e^{5} + \frac{89}{2}e^{4} + \frac{51}{2}e^{3} - 42e^{2} - 12e + 5$ |
| 43 | $[43, 43, 2w^{2} - 3w - 18]$ | $\phantom{-}\frac{1}{2}e^{8} + e^{7} - \frac{9}{2}e^{6} - 8e^{5} + \frac{27}{2}e^{4} + \frac{37}{2}e^{3} - 16e^{2} - 12e + 3$ |
| 47 | $[47, 47, -2w + 7]$ | $\phantom{-}2e^{8} + e^{7} - 23e^{6} - 9e^{5} + 82e^{4} + 25e^{3} - 88e^{2} - 26e + 6$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $-e^{8} + 11e^{6} - e^{5} - 38e^{4} + 6e^{3} + 44e^{2} - 9e - 14$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $-\frac{1}{4}e^{8} + \frac{1}{2}e^{7} + \frac{13}{4}e^{6} - \frac{5}{2}e^{5} - \frac{33}{4}e^{4} + \frac{5}{4}e^{3} - \frac{13}{2}e^{2} + 4e + \frac{25}{2}$ |
| 67 | $[67, 67, -2w^{2} + 5w + 8]$ | $-e^{7} + 11e^{5} + e^{4} - 35e^{3} - 6e^{2} + 30e + 2$ |
| 79 | $[79, 79, w^{2} - 3w - 9]$ | $\phantom{-}\frac{3}{2}e^{8} + e^{7} - \frac{33}{2}e^{6} - 9e^{5} + \frac{113}{2}e^{4} + \frac{51}{2}e^{3} - 60e^{2} - 22e + 5$ |
| 97 | $[97, 97, -w^{2} - 2w + 2]$ | $-e^{7} - e^{6} + 11e^{5} + 5e^{4} - 40e^{3} - 3e^{2} + 43e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -2w^{2} + 3w + 16]$ | $1$ |