Base field \(\Q(\sqrt{241}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 60\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6,6,19w - 157]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + x^{5} - 9x^{4} - 8x^{3} + 21x^{2} + 13x - 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -393w - 2854]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -393w + 3247]$ | $-1$ |
| 3 | $[3, 3, 4w - 33]$ | $-e^{2} + 3$ |
| 3 | $[3, 3, 4w + 29]$ | $\phantom{-}1$ |
| 5 | $[5, 5, 42w + 305]$ | $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3} - \frac{1}{2}e^{2} - 5e + \frac{3}{2}$ |
| 5 | $[5, 5, -42w + 347]$ | $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3} + \frac{1}{2}e^{2} - 5e - \frac{3}{2}$ |
| 29 | $[29, 29, 1820w + 13217]$ | $\phantom{-}\frac{3}{2}e^{5} - e^{4} - \frac{23}{2}e^{3} + \frac{13}{2}e^{2} + 18e - \frac{17}{2}$ |
| 29 | $[29, 29, 1820w - 15037]$ | $\phantom{-}\frac{1}{2}e^{5} + e^{4} - \frac{5}{2}e^{3} - \frac{13}{2}e^{2} + \frac{13}{2}$ |
| 41 | $[41, 41, -80w - 581]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{5}{2}e^{3} + \frac{3}{2}e^{2} - 2e - \frac{13}{2}$ |
| 41 | $[41, 41, 80w - 661]$ | $-\frac{1}{2}e^{5} + e^{4} + \frac{5}{2}e^{3} - \frac{7}{2}e^{2} + 2e - \frac{1}{2}$ |
| 47 | $[47, 47, 34w - 281]$ | $\phantom{-}e^{5} - 2e^{4} - 8e^{3} + 14e^{2} + 17e - 22$ |
| 47 | $[47, 47, 34w + 247]$ | $-e^{5} + 2e^{4} + 7e^{3} - 13e^{2} - 12e + 15$ |
| 49 | $[49, 7, -7]$ | $-\frac{3}{2}e^{5} + e^{4} + \frac{21}{2}e^{3} - \frac{11}{2}e^{2} - 13e + \frac{11}{2}$ |
| 53 | $[53, 53, 6w + 43]$ | $\phantom{-}\frac{3}{2}e^{5} + e^{4} - \frac{25}{2}e^{3} - \frac{13}{2}e^{2} + 21e + \frac{13}{2}$ |
| 53 | $[53, 53, 6w - 49]$ | $-\frac{1}{2}e^{5} + e^{4} + \frac{13}{2}e^{3} - \frac{15}{2}e^{2} - 18e + \frac{15}{2}$ |
| 59 | $[59, 59, 10w + 73]$ | $\phantom{-}e^{3} - 5e - 4$ |
| 59 | $[59, 59, 10w - 83]$ | $\phantom{-}e^{5} - 2e^{4} - 6e^{3} + 12e^{2} + 5e - 14$ |
| 61 | $[61, 61, 4178w + 30341]$ | $-\frac{3}{2}e^{5} + \frac{27}{2}e^{3} - \frac{3}{2}e^{2} - 28e - \frac{3}{2}$ |
| 61 | $[61, 61, 4178w - 34519]$ | $-\frac{1}{2}e^{5} - e^{4} + \frac{7}{2}e^{3} + \frac{9}{2}e^{2} - 5e - \frac{9}{2}$ |
| 67 | $[67, 67, -332w + 2743]$ | $\phantom{-}2e^{5} - e^{4} - 17e^{3} + 7e^{2} + 29e - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,393w - 3247]$ | $1$ |
| $3$ | $[3,3,-4w - 29]$ | $-1$ |