Base field \(\Q(\sqrt{85}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[15,15,-w + 3]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 22x^{4} + 137x^{2} + 196\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-\frac{1}{28}e^{5} - \frac{15}{28}e^{3} - \frac{23}{14}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{1}{8}e^{4} - \frac{17}{8}e^{2} - \frac{11}{2}$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{1}{28}e^{5} - \frac{15}{28}e^{3} - \frac{23}{14}e$ |
| 7 | $[7, 7, w]$ | $-\frac{3}{56}e^{5} - \frac{59}{56}e^{3} - \frac{59}{14}e$ |
| 7 | $[7, 7, w + 6]$ | $-\frac{3}{56}e^{5} - \frac{59}{56}e^{3} - \frac{59}{14}e$ |
| 17 | $[17, 17, w + 8]$ | $-e$ |
| 19 | $[19, 19, w + 1]$ | $-\frac{5}{8}e^{4} - \frac{69}{8}e^{2} - \frac{41}{2}$ |
| 19 | $[19, 19, w - 2]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{13}{4}e^{2} + 3$ |
| 23 | $[23, 23, w + 9]$ | $\phantom{-}\frac{1}{14}e^{5} + \frac{15}{14}e^{3} + \frac{30}{7}e$ |
| 23 | $[23, 23, w + 13]$ | $\phantom{-}\frac{3}{56}e^{5} + \frac{3}{56}e^{3} - \frac{81}{14}e$ |
| 37 | $[37, 37, w + 11]$ | $-\frac{5}{28}e^{5} - \frac{89}{28}e^{3} - \frac{96}{7}e$ |
| 37 | $[37, 37, w + 25]$ | $\phantom{-}\frac{2}{7}e^{5} + \frac{30}{7}e^{3} + \frac{92}{7}e$ |
| 59 | $[59, 59, 3w + 10]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{17}{8}e^{2} + \frac{21}{2}$ |
| 59 | $[59, 59, 3w - 13]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{9}{8}e^{2} - \frac{11}{2}$ |
| 73 | $[73, 73, w + 15]$ | $-\frac{1}{56}e^{5} + \frac{55}{56}e^{3} + \frac{153}{14}e$ |
| 73 | $[73, 73, w + 57]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{17}{4}e^{3} + 16e$ |
| 89 | $[89, 89, -w - 10]$ | $-\frac{1}{2}e^{4} - \frac{15}{2}e^{2} - 18$ |
| 89 | $[89, 89, w - 11]$ | $\phantom{-}\frac{7}{8}e^{4} + \frac{79}{8}e^{2} + \frac{23}{2}$ |
| 97 | $[97, 97, w + 22]$ | $-\frac{11}{56}e^{5} - \frac{179}{56}e^{3} - \frac{95}{14}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 3]$ | $\frac{1}{28}e^{5} + \frac{15}{28}e^{3} + \frac{23}{14}e$ |
| $5$ | $[5,5,-w + 3]$ | $\frac{1}{28}e^{5} + \frac{15}{28}e^{3} + \frac{23}{14}e$ |