Base field \(\Q(\sqrt{55}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 55\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $76$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} - 36x^{16} + 537x^{14} - 4280x^{12} + 19563x^{10} - 50980x^{8} + 70459x^{6} - 44032x^{4} + 10688x^{2} - 512\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -2w + 15]$ | $\phantom{-}\frac{1}{32}e^{14} - \frac{29}{32}e^{12} + \frac{167}{16}e^{10} - \frac{963}{16}e^{8} + \frac{5713}{32}e^{6} - \frac{7869}{32}e^{4} + 112e^{2} - 10$ |
| 11 | $[11, 11, 3w - 22]$ | $\phantom{-}\frac{1}{64}e^{17} - \frac{9}{16}e^{15} + \frac{537}{64}e^{13} - \frac{533}{8}e^{11} + \frac{19195}{64}e^{9} - \frac{11965}{16}e^{7} + \frac{58667}{64}e^{5} - 398e^{3} + 42e$ |
| 13 | $[13, 13, w + 4]$ | $-\frac{1}{64}e^{17} + \frac{17}{32}e^{15} - \frac{475}{64}e^{13} + \frac{219}{4}e^{11} - \frac{14551}{64}e^{9} + \frac{16645}{32}e^{7} - \frac{37261}{64}e^{5} + \frac{3593}{16}e^{3} - 13e$ |
| 13 | $[13, 13, w + 9]$ | $-\frac{1}{64}e^{17} + \frac{17}{32}e^{15} - \frac{475}{64}e^{13} + \frac{219}{4}e^{11} - \frac{14551}{64}e^{9} + \frac{16645}{32}e^{7} - \frac{37261}{64}e^{5} + \frac{3593}{16}e^{3} - 13e$ |
| 17 | $[17, 17, w + 2]$ | $-\frac{1}{8}e^{11} + \frac{11}{4}e^{9} - 22e^{7} + \frac{307}{4}e^{5} - \frac{855}{8}e^{3} + \frac{71}{2}e$ |
| 17 | $[17, 17, w + 15]$ | $-\frac{1}{8}e^{11} + \frac{11}{4}e^{9} - 22e^{7} + \frac{307}{4}e^{5} - \frac{855}{8}e^{3} + \frac{71}{2}e$ |
| 19 | $[19, 19, -w - 6]$ | $\phantom{-}\frac{1}{64}e^{17} - \frac{9}{16}e^{15} + \frac{533}{64}e^{13} - \frac{1043}{16}e^{11} + \frac{18419}{64}e^{9} - \frac{11247}{16}e^{7} + \frac{54487}{64}e^{5} - \frac{6085}{16}e^{3} + \frac{79}{2}e$ |
| 19 | $[19, 19, w - 6]$ | $\phantom{-}\frac{1}{64}e^{17} - \frac{9}{16}e^{15} + \frac{533}{64}e^{13} - \frac{1043}{16}e^{11} + \frac{18419}{64}e^{9} - \frac{11247}{16}e^{7} + \frac{54487}{64}e^{5} - \frac{6085}{16}e^{3} + \frac{79}{2}e$ |
| 23 | $[23, 23, w + 3]$ | $\phantom{-}\frac{1}{32}e^{14} - \frac{29}{32}e^{12} + \frac{167}{16}e^{10} - \frac{967}{16}e^{8} + \frac{5833}{32}e^{6} - \frac{8405}{32}e^{4} + \frac{533}{4}e^{2} - 12$ |
| 23 | $[23, 23, w + 20]$ | $\phantom{-}\frac{1}{32}e^{14} - \frac{29}{32}e^{12} + \frac{167}{16}e^{10} - \frac{967}{16}e^{8} + \frac{5833}{32}e^{6} - \frac{8405}{32}e^{4} + \frac{533}{4}e^{2} - 12$ |
| 47 | $[47, 47, w + 14]$ | $\phantom{-}\frac{1}{32}e^{16} - \frac{35}{32}e^{14} + \frac{125}{8}e^{12} - \frac{1873}{16}e^{10} + \frac{15693}{32}e^{8} - \frac{35979}{32}e^{6} + \frac{19999}{16}e^{4} - \frac{927}{2}e^{2} + 24$ |
| 47 | $[47, 47, w + 33]$ | $\phantom{-}\frac{1}{32}e^{16} - \frac{35}{32}e^{14} + \frac{125}{8}e^{12} - \frac{1873}{16}e^{10} + \frac{15693}{32}e^{8} - \frac{35979}{32}e^{6} + \frac{19999}{16}e^{4} - \frac{927}{2}e^{2} + 24$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{16}e^{14} - \frac{27}{16}e^{12} + \frac{143}{8}e^{10} - \frac{747}{8}e^{8} + \frac{3917}{16}e^{6} - \frac{4463}{16}e^{4} + \frac{285}{4}e^{2} + 10$ |
| 67 | $[67, 67, w + 16]$ | $-\frac{1}{32}e^{16} + \frac{17}{16}e^{14} - \frac{475}{32}e^{12} + \frac{875}{8}e^{10} - \frac{14479}{32}e^{8} + \frac{16437}{16}e^{6} - \frac{36501}{32}e^{4} + \frac{1809}{4}e^{2} - 38$ |
| 67 | $[67, 67, w + 51]$ | $-\frac{1}{32}e^{16} + \frac{17}{16}e^{14} - \frac{475}{32}e^{12} + \frac{875}{8}e^{10} - \frac{14479}{32}e^{8} + \frac{16437}{16}e^{6} - \frac{36501}{32}e^{4} + \frac{1809}{4}e^{2} - 38$ |
| 73 | $[73, 73, w + 36]$ | $-\frac{1}{32}e^{17} + \frac{9}{8}e^{15} - \frac{535}{32}e^{13} + \frac{2109}{16}e^{11} - \frac{18807}{32}e^{9} + \frac{5801}{4}e^{7} - \frac{56369}{32}e^{5} + \frac{12093}{16}e^{3} - 67e$ |
| 73 | $[73, 73, w + 37]$ | $-\frac{1}{32}e^{17} + \frac{9}{8}e^{15} - \frac{535}{32}e^{13} + \frac{2109}{16}e^{11} - \frac{18807}{32}e^{9} + \frac{5801}{4}e^{7} - \frac{56369}{32}e^{5} + \frac{12093}{16}e^{3} - 67e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-1$ |
| $3$ | $[3, 3, w + 2]$ | $-1$ |