Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[12, 6, 2w + 12]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + x^{5} - 10x^{4} - 3x^{3} + 16x^{2} - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 6]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -3w - 17]$ | $-\frac{2}{5}e^{5} - \frac{1}{5}e^{4} + \frac{23}{5}e^{3} - \frac{3}{5}e^{2} - \frac{48}{5}e + \frac{14}{5}$ |
| 11 | $[11, 11, 3w - 20]$ | $-\frac{3}{5}e^{5} - \frac{4}{5}e^{4} + \frac{27}{5}e^{3} + \frac{13}{5}e^{2} - \frac{27}{5}e + \frac{6}{5}$ |
| 13 | $[13, 13, 2w - 13]$ | $-\frac{8}{5}e^{5} - \frac{9}{5}e^{4} + \frac{77}{5}e^{3} + \frac{33}{5}e^{2} - \frac{107}{5}e - \frac{9}{5}$ |
| 13 | $[13, 13, 2w + 11]$ | $\phantom{-}\frac{2}{5}e^{5} + \frac{1}{5}e^{4} - \frac{23}{5}e^{3} - \frac{2}{5}e^{2} + \frac{43}{5}e + \frac{1}{5}$ |
| 17 | $[17, 17, w + 7]$ | $\phantom{-}\frac{4}{5}e^{5} + \frac{2}{5}e^{4} - \frac{41}{5}e^{3} + \frac{6}{5}e^{2} + \frac{61}{5}e + \frac{2}{5}$ |
| 17 | $[17, 17, -w + 8]$ | $-\frac{11}{5}e^{5} - \frac{13}{5}e^{4} + \frac{104}{5}e^{3} + \frac{46}{5}e^{2} - \frac{144}{5}e - \frac{3}{5}$ |
| 19 | $[19, 19, -w - 4]$ | $\phantom{-}e^{3} + 2e^{2} - 7e - 5$ |
| 19 | $[19, 19, -w + 5]$ | $\phantom{-}e^{5} + e^{4} - 10e^{3} - 3e^{2} + 18e + 1$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{2}{5}e^{5} + \frac{1}{5}e^{4} - \frac{18}{5}e^{3} + \frac{3}{5}e^{2} + \frac{13}{5}e - \frac{4}{5}$ |
| 31 | $[31, 31, -6w - 35]$ | $\phantom{-}\frac{4}{5}e^{5} + \frac{7}{5}e^{4} - \frac{31}{5}e^{3} - \frac{34}{5}e^{2} + \frac{21}{5}e + \frac{27}{5}$ |
| 31 | $[31, 31, -6w + 41]$ | $\phantom{-}\frac{7}{5}e^{5} + \frac{6}{5}e^{4} - \frac{73}{5}e^{3} - \frac{17}{5}e^{2} + \frac{128}{5}e + \frac{16}{5}$ |
| 37 | $[37, 37, -w - 1]$ | $\phantom{-}e^{5} + e^{4} - 10e^{3} - 4e^{2} + 16e$ |
| 37 | $[37, 37, w - 2]$ | $\phantom{-}\frac{1}{5}e^{5} + \frac{3}{5}e^{4} - \frac{9}{5}e^{3} - \frac{21}{5}e^{2} + \frac{14}{5}e + \frac{28}{5}$ |
| 47 | $[47, 47, 3w + 16]$ | $-e^{5} + 11e^{3} - 5e^{2} - 18e + 4$ |
| 47 | $[47, 47, -3w + 19]$ | $\phantom{-}\frac{9}{5}e^{5} + \frac{12}{5}e^{4} - \frac{86}{5}e^{3} - \frac{49}{5}e^{2} + \frac{141}{5}e - \frac{3}{5}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{3}{5}e^{5} + \frac{4}{5}e^{4} - \frac{32}{5}e^{3} - \frac{23}{5}e^{2} + \frac{57}{5}e + \frac{19}{5}$ |
| 67 | $[67, 67, 3w - 22]$ | $-\frac{7}{5}e^{5} - \frac{11}{5}e^{4} + \frac{63}{5}e^{3} + \frac{52}{5}e^{2} - \frac{93}{5}e - \frac{16}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 6]$ | $-1$ |
| $4$ | $[4, 2, 2]$ | $-1$ |