Base field \(\Q(\sqrt{34}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[12,6,-2w + 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 23x^{8} + 185x^{6} + 624x^{4} + 832x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{16}e^{9} + \frac{5}{4}e^{7} + \frac{31}{4}e^{5} + \frac{237}{16}e^{3} + \frac{7}{2}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{13}{64}e^{9} + \frac{259}{64}e^{7} + \frac{1613}{64}e^{5} + \frac{401}{8}e^{3} + 17e$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{9}{64}e^{9} - \frac{183}{64}e^{7} - \frac{1177}{64}e^{5} - \frac{315}{8}e^{3} - 19e$ |
| 11 | $[11, 11, w + 1]$ | $-e$ |
| 11 | $[11, 11, w + 10]$ | $-\frac{1}{16}e^{9} - \frac{19}{16}e^{7} - \frac{109}{16}e^{5} - \frac{47}{4}e^{3} - 4e$ |
| 17 | $[17, 17, -3w + 17]$ | $\phantom{-}\frac{1}{16}e^{8} + \frac{23}{16}e^{6} + \frac{169}{16}e^{4} + 26e^{2} + 14$ |
| 29 | $[29, 29, w + 11]$ | $\phantom{-}\frac{11}{64}e^{9} + \frac{229}{64}e^{7} + \frac{1547}{64}e^{5} + \frac{463}{8}e^{3} + 36e$ |
| 29 | $[29, 29, w + 18]$ | $\phantom{-}\frac{29}{64}e^{9} + \frac{579}{64}e^{7} + \frac{3597}{64}e^{5} + \frac{875}{8}e^{3} + 30e$ |
| 37 | $[37, 37, w + 16]$ | $-\frac{15}{64}e^{9} - \frac{305}{64}e^{7} - \frac{1983}{64}e^{5} - \frac{549}{8}e^{3} - 34e$ |
| 37 | $[37, 37, w + 21]$ | $-\frac{1}{64}e^{9} - \frac{31}{64}e^{7} - \frac{305}{64}e^{5} - \frac{135}{8}e^{3} - 16e$ |
| 47 | $[47, 47, -w - 9]$ | $-e^{2}$ |
| 47 | $[47, 47, w - 9]$ | $\phantom{-}\frac{3}{8}e^{8} + \frac{61}{8}e^{6} + \frac{387}{8}e^{4} + 99e^{2} + 44$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{11}{16}e^{8} + \frac{221}{16}e^{6} + \frac{1395}{16}e^{4} + 178e^{2} + 66$ |
| 61 | $[61, 61, w + 20]$ | $\phantom{-}\frac{19}{64}e^{9} + \frac{381}{64}e^{7} + \frac{2419}{64}e^{5} + \frac{635}{8}e^{3} + 30e$ |
| 61 | $[61, 61, w + 41]$ | $\phantom{-}\frac{13}{64}e^{9} + \frac{259}{64}e^{7} + \frac{1613}{64}e^{5} + \frac{401}{8}e^{3} + 16e$ |
| 89 | $[89, 89, 2w - 15]$ | $\phantom{-}\frac{1}{16}e^{8} + \frac{23}{16}e^{6} + \frac{153}{16}e^{4} + 17e^{2} + 6$ |
| 89 | $[89, 89, -2w - 15]$ | $\phantom{-}\frac{5}{16}e^{8} + \frac{99}{16}e^{6} + \frac{605}{16}e^{4} + 71e^{2} + 14$ |
| 103 | $[103, 103, -14w + 81]$ | $\phantom{-}\frac{7}{4}e^{8} + \frac{141}{4}e^{6} + \frac{887}{4}e^{4} + 440e^{2} + 136$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w - 6]$ | $-1$ |
| $3$ | $[3,3,-w + 1]$ | $-\frac{1}{16}e^{9} - \frac{5}{4}e^{7} - \frac{31}{4}e^{5} - \frac{237}{16}e^{3} - \frac{7}{2}e$ |