Base field 3.3.785.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[24, 6, 2w - 4]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 4x^{4} - 8x^{3} + 26x^{2} + 19x - 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 3]$ | $-\frac{4}{19}e^{4} + \frac{18}{19}e^{3} + \frac{23}{19}e^{2} - \frac{106}{19}e - \frac{42}{19}$ |
| 8 | $[8, 2, 2]$ | $-1$ |
| 9 | $[9, 3, w^{2} + w - 4]$ | $-\frac{2}{19}e^{4} + \frac{9}{19}e^{3} + \frac{21}{19}e^{2} - \frac{72}{19}e - \frac{59}{19}$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{19}e^{4} + \frac{5}{19}e^{3} - \frac{39}{19}e^{2} - \frac{21}{19}e + \frac{134}{19}$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{1}{19}e^{4} - \frac{5}{19}e^{3} + \frac{20}{19}e^{2} + \frac{40}{19}e + \frac{18}{19}$ |
| 23 | $[23, 23, w^{2} - 2]$ | $\phantom{-}\frac{4}{19}e^{4} - \frac{18}{19}e^{3} - \frac{23}{19}e^{2} + \frac{87}{19}e + \frac{99}{19}$ |
| 23 | $[23, 23, w^{2} - 3]$ | $\phantom{-}\frac{4}{19}e^{4} - \frac{18}{19}e^{3} - \frac{4}{19}e^{2} + \frac{68}{19}e - \frac{72}{19}$ |
| 23 | $[23, 23, -w^{2} + 8]$ | $\phantom{-}\frac{4}{19}e^{4} - \frac{18}{19}e^{3} - \frac{23}{19}e^{2} + \frac{87}{19}e + \frac{99}{19}$ |
| 29 | $[29, 29, w - 4]$ | $-\frac{11}{19}e^{4} + \frac{40}{19}e^{3} + \frac{87}{19}e^{2} - \frac{263}{19}e - \frac{87}{19}$ |
| 37 | $[37, 37, w^{2} + w - 8]$ | $\phantom{-}\frac{5}{19}e^{4} - \frac{32}{19}e^{3} - \frac{5}{19}e^{2} + \frac{199}{19}e + \frac{5}{19}$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $-\frac{15}{19}e^{4} + \frac{58}{19}e^{3} + \frac{91}{19}e^{2} - \frac{255}{19}e - \frac{129}{19}$ |
| 47 | $[47, 47, 2w^{2} + w - 8]$ | $\phantom{-}\frac{10}{19}e^{4} - \frac{26}{19}e^{3} - \frac{86}{19}e^{2} + \frac{94}{19}e + \frac{162}{19}$ |
| 59 | $[59, 59, -2w^{2} - 3w + 6]$ | $\phantom{-}\frac{4}{19}e^{4} - \frac{18}{19}e^{3} - \frac{23}{19}e^{2} + \frac{163}{19}e - \frac{15}{19}$ |
| 61 | $[61, 61, -2w - 1]$ | $-\frac{10}{19}e^{4} + \frac{45}{19}e^{3} + \frac{67}{19}e^{2} - \frac{284}{19}e - \frac{67}{19}$ |
| 67 | $[67, 67, -2w - 3]$ | $\phantom{-}\frac{3}{19}e^{4} - \frac{4}{19}e^{3} - \frac{79}{19}e^{2} + \frac{108}{19}e + \frac{269}{19}$ |
| 79 | $[79, 79, 2w^{2} - 9]$ | $-\frac{2}{19}e^{4} - \frac{10}{19}e^{3} + \frac{78}{19}e^{2} + \frac{42}{19}e - \frac{154}{19}$ |
| 109 | $[109, 109, w^{2} + 2w - 6]$ | $-\frac{6}{19}e^{4} + \frac{8}{19}e^{3} + \frac{82}{19}e^{2} + \frac{12}{19}e - \frac{196}{19}$ |
| 109 | $[109, 109, 2w^{2} + w - 14]$ | $-\frac{2}{19}e^{4} + \frac{9}{19}e^{3} + \frac{21}{19}e^{2} - \frac{110}{19}e + \frac{131}{19}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 2]$ | $-1$ |
| $8$ | $[8, 2, 2]$ | $1$ |