Base field 3.3.1825.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, -w^{2} - w + 3]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $70$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 10x^{8} + 28x^{7} - 15x^{6} - 183x^{5} - 242x^{4} - 15x^{3} + 119x^{2} + 21x - 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w]$ | $-\frac{4}{3}e^{8} - \frac{37}{3}e^{7} - 28e^{6} + 40e^{5} + \frac{614}{3}e^{4} + 162e^{3} - \frac{155}{3}e^{2} - \frac{154}{3}e + 10$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{2}{3}e^{8} + \frac{17}{3}e^{7} + \frac{32}{3}e^{6} - 22e^{5} - 82e^{4} - \frac{157}{3}e^{3} + 15e^{2} + \frac{25}{3}e + 1$ |
| 11 | $[11, 11, w + 2]$ | $-\frac{7}{3}e^{8} - \frac{61}{3}e^{7} - \frac{121}{3}e^{6} + 78e^{5} + 313e^{4} + \frac{593}{3}e^{3} - 108e^{2} - \frac{179}{3}e + 18$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{4}{3}e^{8} + \frac{37}{3}e^{7} + 28e^{6} - 40e^{5} - \frac{614}{3}e^{4} - 162e^{3} + \frac{155}{3}e^{2} + \frac{151}{3}e - 12$ |
| 17 | $[17, 17, -w^{2} - w + 4]$ | $-\frac{5}{3}e^{8} - 15e^{7} - \frac{94}{3}e^{6} + \frac{172}{3}e^{5} + \frac{724}{3}e^{4} + \frac{436}{3}e^{3} - 96e^{2} - 41e + 18$ |
| 23 | $[23, 23, -w^{2} + 6]$ | $\phantom{-}e^{8} + \frac{28}{3}e^{7} + \frac{62}{3}e^{6} - \frac{106}{3}e^{5} - \frac{478}{3}e^{4} - 93e^{3} + 81e^{2} + \frac{95}{3}e - 22$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-1$ |
| 23 | $[23, 23, -w + 4]$ | $\phantom{-}\frac{2}{3}e^{8} + \frac{19}{3}e^{7} + \frac{47}{3}e^{6} - \frac{47}{3}e^{5} - \frac{319}{3}e^{4} - \frac{329}{3}e^{3} - \frac{13}{3}e^{2} + \frac{70}{3}e + 6$ |
| 27 | $[27, 3, 3]$ | $-2e^{8} - 17e^{7} - \frac{86}{3}e^{6} + 88e^{5} + \frac{782}{3}e^{4} + \frac{109}{3}e^{3} - \frac{695}{3}e^{2} - \frac{125}{3}e + 50$ |
| 29 | $[29, 29, -w^{2} - 2w + 4]$ | $-\frac{1}{3}e^{8} - \frac{7}{3}e^{7} - \frac{2}{3}e^{6} + 22e^{5} + \frac{82}{3}e^{4} - \frac{158}{3}e^{3} - \frac{232}{3}e^{2} + 11e + 20$ |
| 31 | $[31, 31, w^{2} - 10]$ | $-e^{8} - \frac{26}{3}e^{7} - 17e^{6} + \frac{98}{3}e^{5} + \frac{385}{3}e^{4} + \frac{259}{3}e^{3} - \frac{56}{3}e^{2} - 20e - 6$ |
| 41 | $[41, 41, w + 4]$ | $\phantom{-}\frac{4}{3}e^{8} + \frac{31}{3}e^{7} + 12e^{6} - 67e^{5} - \frac{428}{3}e^{4} + 52e^{3} + \frac{617}{3}e^{2} + \frac{64}{3}e - 46$ |
| 41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}\frac{4}{3}e^{8} + 12e^{7} + 25e^{6} - \frac{140}{3}e^{5} - 196e^{4} - \frac{349}{3}e^{3} + \frac{283}{3}e^{2} + \frac{163}{3}e - 12$ |
| 41 | $[41, 41, -2w - 5]$ | $\phantom{-}\frac{10}{3}e^{8} + \frac{86}{3}e^{7} + 53e^{6} - \frac{379}{3}e^{5} - \frac{1318}{3}e^{4} - \frac{563}{3}e^{3} + 253e^{2} + \frac{259}{3}e - 48$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{4}{3}e^{8} - 11e^{7} - \frac{53}{3}e^{6} + \frac{167}{3}e^{5} + \frac{485}{3}e^{4} + \frac{101}{3}e^{3} - 135e^{2} - 38e + 32$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}4e^{8} + \frac{106}{3}e^{7} + \frac{211}{3}e^{6} - \frac{433}{3}e^{5} - 562e^{4} - \frac{892}{3}e^{3} + \frac{869}{3}e^{2} + \frac{385}{3}e - 62$ |
| 49 | $[49, 7, w^{2} - w - 8]$ | $\phantom{-}\frac{7}{3}e^{8} + 21e^{7} + 44e^{6} - \frac{239}{3}e^{5} - 339e^{4} - \frac{625}{3}e^{3} + \frac{412}{3}e^{2} + \frac{193}{3}e - 28$ |
| 53 | $[53, 53, 2w^{2} + w - 12]$ | $\phantom{-}\frac{2}{3}e^{8} + \frac{17}{3}e^{7} + \frac{35}{3}e^{6} - 16e^{5} - 81e^{4} - \frac{265}{3}e^{3} - 20e^{2} + \frac{61}{3}e + 8$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-5e^{8} - \frac{131}{3}e^{7} - 85e^{6} + \frac{539}{3}e^{5} + \frac{2041}{3}e^{4} + \frac{1075}{3}e^{3} - \frac{977}{3}e^{2} - 139e + 52$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{2} - w + 3]$ | $1$ |