Base field 3.3.1489.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, w - 2]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $50$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 5x^{8} - 17x^{7} - 105x^{6} - 20x^{5} + 376x^{4} + 208x^{3} - 384x^{2} - 128x + 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-\frac{3}{32}e^{7} - \frac{3}{8}e^{6} + \frac{57}{32}e^{5} + \frac{119}{16}e^{4} - \frac{7}{4}e^{3} - \frac{43}{2}e^{2} - 6e + 11$ |
| 13 | $[13, 13, w^{2} - 3w - 5]$ | $-\frac{3}{64}e^{8} - \frac{13}{32}e^{7} + \frac{5}{64}e^{6} + \frac{65}{8}e^{5} + \frac{61}{4}e^{4} - \frac{79}{4}e^{3} - 51e^{2} + 3e + 24$ |
| 17 | $[17, 17, w - 1]$ | $\phantom{-}\frac{1}{64}e^{8} + \frac{9}{32}e^{7} + \frac{29}{64}e^{6} - \frac{91}{16}e^{5} - \frac{227}{16}e^{4} + \frac{103}{8}e^{3} + 40e^{2} - 16$ |
| 19 | $[19, 19, -w^{2} + 2w + 6]$ | $-\frac{3}{64}e^{8} - \frac{3}{16}e^{7} + \frac{65}{64}e^{6} + \frac{127}{32}e^{5} - \frac{15}{4}e^{4} - \frac{59}{4}e^{3} + 8e^{2} + 10e - 10$ |
| 19 | $[19, 19, -w^{2} + 2w + 10]$ | $-\frac{1}{64}e^{8} - \frac{1}{32}e^{7} + \frac{27}{64}e^{6} + \frac{9}{16}e^{5} - \frac{47}{16}e^{4} - \frac{5}{4}e^{3} + \frac{17}{2}e^{2} - 6$ |
| 19 | $[19, 19, -w + 3]$ | $\phantom{-}\frac{5}{64}e^{8} + \frac{7}{32}e^{7} - \frac{107}{64}e^{6} - 4e^{5} + \frac{37}{8}e^{4} + 9e^{3} - e^{2} + 2$ |
| 23 | $[23, 23, w - 2]$ | $-1$ |
| 27 | $[27, 3, 3]$ | $-\frac{1}{64}e^{8} + \frac{3}{32}e^{7} + \frac{47}{64}e^{6} - \frac{33}{16}e^{5} - \frac{33}{4}e^{4} + \frac{19}{4}e^{3} + \frac{35}{2}e^{2} + 2e - 10$ |
| 29 | $[29, 29, w^{2} - 2w - 5]$ | $\phantom{-}\frac{1}{16}e^{8} + \frac{19}{32}e^{7} - \frac{1}{16}e^{6} - \frac{389}{32}e^{5} - \frac{333}{16}e^{4} + \frac{259}{8}e^{3} + 69e^{2} - 5e - 32$ |
| 31 | $[31, 31, w^{2} - 3w - 6]$ | $\phantom{-}\frac{1}{64}e^{8} - \frac{3}{32}e^{7} - \frac{47}{64}e^{6} + \frac{33}{16}e^{5} + \frac{33}{4}e^{4} - \frac{19}{4}e^{3} - \frac{35}{2}e^{2} - 2e + 10$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}\frac{1}{16}e^{8} + \frac{11}{32}e^{7} - \frac{7}{8}e^{6} - \frac{221}{32}e^{5} - \frac{39}{8}e^{4} + \frac{77}{4}e^{3} + 21e^{2} - 8e - 12$ |
| 31 | $[31, 31, w^{2} - 2w - 4]$ | $-\frac{1}{64}e^{8} - \frac{9}{32}e^{7} - \frac{25}{64}e^{6} + \frac{93}{16}e^{5} + \frac{103}{8}e^{4} - \frac{59}{4}e^{3} - \frac{75}{2}e^{2} - e + 14$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{13}{64}e^{8} + \frac{25}{32}e^{7} - \frac{251}{64}e^{6} - \frac{245}{16}e^{5} + \frac{39}{8}e^{4} + \frac{337}{8}e^{3} + \frac{21}{2}e^{2} - 16e - 4$ |
| 43 | $[43, 43, w^{2} - 3w - 10]$ | $-\frac{1}{32}e^{8} + \frac{1}{8}e^{7} + \frac{51}{32}e^{6} - \frac{39}{16}e^{5} - \frac{83}{4}e^{4} + e^{3} + 61e^{2} + 10e - 36$ |
| 47 | $[47, 47, -w - 4]$ | $\phantom{-}\frac{1}{16}e^{8} + \frac{3}{16}e^{7} - \frac{23}{16}e^{6} - \frac{61}{16}e^{5} + 6e^{4} + 14e^{3} - \frac{17}{2}e^{2} - 14e + 4$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}\frac{3}{16}e^{8} + \frac{35}{32}e^{7} - \frac{21}{8}e^{6} - \frac{717}{32}e^{5} - 14e^{4} + \frac{267}{4}e^{3} + 58e^{2} - 32e - 18$ |
| 47 | $[47, 47, -2w^{2} + 3w + 17]$ | $-\frac{21}{64}e^{8} - \frac{11}{8}e^{7} + \frac{383}{64}e^{6} + \frac{875}{32}e^{5} - \frac{5}{8}e^{4} - \frac{315}{4}e^{3} - 44e^{2} + 33e + 16$ |
| 49 | $[49, 7, w^{2} - w - 10]$ | $-\frac{5}{32}e^{8} - \frac{25}{32}e^{7} + \frac{77}{32}e^{6} + \frac{497}{32}e^{5} + \frac{65}{8}e^{4} - \frac{337}{8}e^{3} - 42e^{2} + 19e + 14$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $-\frac{1}{64}e^{8} - \frac{3}{32}e^{7} + \frac{15}{64}e^{6} + 2e^{5} + \frac{3}{4}e^{4} - \frac{57}{8}e^{3} - \frac{5}{2}e^{2} + 4e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, w - 2]$ | $1$ |