Base field 5.5.122821.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[23, 23, -w^{3} + 2w^{2} + 2w - 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 2x^{7} - 12x^{6} - 20x^{5} + 34x^{4} + 40x^{3} - 25x^{2} - 8x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{4} - 2w^{3} - 3w^{2} + 2w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $\phantom{-}\frac{9}{4}e^{7} + \frac{11}{2}e^{6} - \frac{49}{2}e^{5} - 56e^{4} + 51e^{3} + \frac{227}{2}e^{2} - \frac{21}{4}e - \frac{43}{2}$ |
| 11 | $[11, 11, -w^{2} + w + 2]$ | $-\frac{5}{2}e^{7} - 6e^{6} + \frac{55}{2}e^{5} + \frac{121}{2}e^{4} - 60e^{3} - \frac{239}{2}e^{2} + 13e + 19$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $-\frac{1}{2}e^{7} - e^{6} + \frac{11}{2}e^{5} + \frac{19}{2}e^{4} - 11e^{3} - \frac{33}{2}e^{2} - 3e - 1$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + w - 3]$ | $-e - 1$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 3w^{2} + w + 2]$ | $-\frac{9}{4}e^{7} - \frac{11}{2}e^{6} + \frac{49}{2}e^{5} + 56e^{4} - 51e^{3} - \frac{227}{2}e^{2} + \frac{25}{4}e + \frac{43}{2}$ |
| 23 | $[23, 23, w^{4} - 3w^{3} - w^{2} + 5w - 3]$ | $-\frac{5}{4}e^{7} - \frac{7}{2}e^{6} + 13e^{5} + \frac{73}{2}e^{4} - 23e^{3} - 78e^{2} - \frac{25}{4}e + \frac{37}{2}$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 2w - 2]$ | $-1$ |
| 29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 4w - 1]$ | $\phantom{-}\frac{15}{4}e^{7} + \frac{19}{2}e^{6} - \frac{81}{2}e^{5} - 97e^{4} + 83e^{3} + \frac{395}{2}e^{2} - \frac{31}{4}e - \frac{77}{2}$ |
| 37 | $[37, 37, w^{4} - 3w^{3} - w^{2} + 5w]$ | $-2e^{7} - 5e^{6} + \frac{43}{2}e^{5} + \frac{103}{2}e^{4} - 42e^{3} - \frac{219}{2}e^{2} - \frac{7}{2}e + 27$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 4w^{2} + 3w + 1]$ | $\phantom{-}\frac{17}{4}e^{7} + \frac{21}{2}e^{6} - 46e^{5} - \frac{213}{2}e^{4} + 94e^{3} + 214e^{2} - \frac{27}{4}e - \frac{79}{2}$ |
| 49 | $[49, 7, -2w^{3} + 4w^{2} + 6w - 5]$ | $-\frac{9}{4}e^{7} - 6e^{6} + 24e^{5} + 62e^{4} - \frac{93}{2}e^{3} - 129e^{2} - \frac{11}{4}e + \frac{53}{2}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + w^{2} - 7w + 3]$ | $\phantom{-}\frac{21}{4}e^{7} + 13e^{6} - \frac{115}{2}e^{5} - \frac{265}{2}e^{4} + \frac{247}{2}e^{3} + \frac{535}{2}e^{2} - \frac{83}{4}e - \frac{93}{2}$ |
| 67 | $[67, 67, w^{3} - 2w^{2} - w + 3]$ | $-\frac{19}{4}e^{7} - \frac{23}{2}e^{6} + 52e^{5} + \frac{235}{2}e^{4} - 110e^{3} - 243e^{2} + \frac{41}{4}e + \frac{107}{2}$ |
| 67 | $[67, 67, -w^{4} + 3w^{3} + 2w^{2} - 6w - 1]$ | $\phantom{-}\frac{7}{4}e^{7} + \frac{9}{2}e^{6} - 19e^{5} - \frac{93}{2}e^{4} + 39e^{3} + 98e^{2} + \frac{3}{4}e - \frac{45}{2}$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 4]$ | $\phantom{-}6e^{7} + 14e^{6} - \frac{133}{2}e^{5} - \frac{283}{2}e^{4} + 147e^{3} + \frac{565}{2}e^{2} - \frac{67}{2}e - 48$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 8w - 2]$ | $\phantom{-}\frac{13}{4}e^{7} + 7e^{6} - \frac{73}{2}e^{5} - \frac{139}{2}e^{4} + \frac{167}{2}e^{3} + \frac{275}{2}e^{2} - \frac{87}{4}e - \frac{63}{2}$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 6w - 2]$ | $\phantom{-}e^{7} + 3e^{6} - 9e^{5} - 30e^{4} + 4e^{3} + 57e^{2} + 32e - 14$ |
| 103 | $[103, 103, w^{3} - 3w^{2} - 2w + 2]$ | $-\frac{9}{2}e^{7} - 11e^{6} + 49e^{5} + 112e^{4} - 103e^{3} - 228e^{2} + \frac{35}{2}e + 40$ |
| 113 | $[113, 113, -2w^{4} + 4w^{3} + 7w^{2} - 7w - 2]$ | $\phantom{-}\frac{5}{2}e^{7} + \frac{13}{2}e^{6} - \frac{51}{2}e^{5} - 65e^{4} + \frac{77}{2}e^{3} + \frac{249}{2}e^{2} + \frac{55}{2}e - 23$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{3} + 2w^{2} + 2w - 2]$ | $1$ |