Base field 3.3.621.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, -2w^{2} + w + 10]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 5x^{9} - 3x^{8} + 46x^{7} - 34x^{6} - 118x^{5} + 141x^{4} + 65x^{3} - 120x^{2} + 38x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-\frac{3}{2}e^{9} + 5e^{8} + \frac{25}{2}e^{7} - \frac{95}{2}e^{6} - \frac{49}{2}e^{5} + \frac{261}{2}e^{4} - 8e^{3} - \frac{197}{2}e^{2} + \frac{73}{2}e - \frac{1}{2}$ |
| 4 | $[4, 2, -w^{2} + w + 5]$ | $-\frac{3}{2}e^{9} + 6e^{8} + \frac{19}{2}e^{7} - \frac{113}{2}e^{6} + \frac{7}{2}e^{5} + \frac{307}{2}e^{4} - 82e^{3} - \frac{225}{2}e^{2} + \frac{173}{2}e - \frac{23}{2}$ |
| 7 | $[7, 7, -w + 2]$ | $-e^{9} + 3e^{8} + 9e^{7} - 28e^{6} - 22e^{5} + 73e^{4} + 7e^{3} - 45e^{2} + 20e - 4$ |
| 19 | $[19, 19, -2w^{2} + w + 10]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{2} + 8]$ | $\phantom{-}2e^{9} - 5e^{8} - 21e^{7} + 47e^{6} + 71e^{5} - 123e^{4} - 79e^{3} + 75e^{2} - 6e + 3$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}\frac{1}{2}e^{9} - 2e^{8} - \frac{7}{2}e^{7} + \frac{39}{2}e^{6} + \frac{3}{2}e^{5} - \frac{111}{2}e^{4} + 23e^{3} + \frac{83}{2}e^{2} - \frac{65}{2}e + \frac{15}{2}$ |
| 29 | $[29, 29, -w^{2} + 2w + 4]$ | $-\frac{3}{2}e^{9} + 6e^{8} + \frac{19}{2}e^{7} - \frac{113}{2}e^{6} + \frac{9}{2}e^{5} + \frac{305}{2}e^{4} - 91e^{3} - \frac{211}{2}e^{2} + \frac{207}{2}e - \frac{39}{2}$ |
| 37 | $[37, 37, w^{2} - 2w - 8]$ | $\phantom{-}4e^{9} - 14e^{8} - 31e^{7} + 131e^{6} + 43e^{5} - 347e^{4} + 86e^{3} + 231e^{2} - 156e + 23$ |
| 41 | $[41, 41, 4w^{2} - 3w - 20]$ | $\phantom{-}3e^{9} - 7e^{8} - 33e^{7} + 64e^{6} + 124e^{5} - 157e^{4} - 179e^{3} + 79e^{2} + 46e - 6$ |
| 43 | $[43, 43, -w - 4]$ | $\phantom{-}\frac{5}{2}e^{9} - 6e^{8} - \frac{55}{2}e^{7} + \frac{115}{2}e^{6} + \frac{203}{2}e^{5} - \frac{315}{2}e^{4} - 140e^{3} + \frac{233}{2}e^{2} + \frac{71}{2}e - \frac{29}{2}$ |
| 47 | $[47, 47, 2w - 1]$ | $-3e^{9} + 6e^{8} + 36e^{7} - 55e^{6} - 152e^{5} + 135e^{4} + 253e^{3} - 71e^{2} - 97e + 24$ |
| 49 | $[49, 7, -2w^{2} + 3w + 4]$ | $\phantom{-}\frac{1}{2}e^{9} - e^{8} - \frac{11}{2}e^{7} + \frac{19}{2}e^{6} + \frac{37}{2}e^{5} - \frac{51}{2}e^{4} - 14e^{3} + \frac{31}{2}e^{2} - \frac{33}{2}e + \frac{1}{2}$ |
| 59 | $[59, 59, 2w^{2} - 13]$ | $-e^{9} + 7e^{8} - 2e^{7} - 67e^{6} + 82e^{5} + 189e^{4} - 274e^{3} - 145e^{2} + 219e - 36$ |
| 61 | $[61, 61, -3w^{2} + 4w + 10]$ | $\phantom{-}\frac{17}{2}e^{9} - 31e^{8} - \frac{125}{2}e^{7} + \frac{585}{2}e^{6} + \frac{117}{2}e^{5} - \frac{1583}{2}e^{4} + 271e^{3} + \frac{1127}{2}e^{2} - \frac{759}{2}e + \frac{97}{2}$ |
| 67 | $[67, 67, 2w^{2} - 2w - 7]$ | $\phantom{-}\frac{3}{2}e^{9} - 8e^{8} - \frac{9}{2}e^{7} + \frac{153}{2}e^{6} - \frac{99}{2}e^{5} - \frac{431}{2}e^{4} + 199e^{3} + \frac{341}{2}e^{2} - \frac{309}{2}e + \frac{49}{2}$ |
| 71 | $[71, 71, -3w - 4]$ | $-\frac{7}{2}e^{9} + 9e^{8} + \frac{73}{2}e^{7} - \frac{171}{2}e^{6} - \frac{249}{2}e^{5} + \frac{463}{2}e^{4} + 154e^{3} - \frac{333}{2}e^{2} - \frac{53}{2}e + \frac{39}{2}$ |
| 79 | $[79, 79, 2w^{2} - 3w - 8]$ | $\phantom{-}12e^{9} - 41e^{8} - 97e^{7} + 389e^{6} + 165e^{5} - 1063e^{4} + 159e^{3} + 781e^{2} - 370e + 29$ |
| 83 | $[83, 83, 2w^{2} - w - 14]$ | $\phantom{-}\frac{7}{2}e^{9} - 14e^{8} - \frac{45}{2}e^{7} + \frac{265}{2}e^{6} - \frac{11}{2}e^{5} - \frac{725}{2}e^{4} + 184e^{3} + \frac{539}{2}e^{2} - \frac{383}{2}e + \frac{45}{2}$ |
| 83 | $[83, 83, -4w^{2} + 3w + 22]$ | $-e^{9} + 5e^{8} + 4e^{7} - 48e^{6} + 23e^{5} + 137e^{4} - 104e^{3} - 115e^{2} + 82e - 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -2w^{2} + w + 10]$ | $-1$ |