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: | $[10, 10, w + 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 27x^{8} + 251x^{6} + 937x^{4} + 1176x^{2} + 400\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{3}{160}e^{9} + \frac{51}{160}e^{7} + \frac{153}{160}e^{5} - \frac{499}{160}e^{3} - \frac{223}{40}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{1}{80}e^{9} + \frac{17}{80}e^{7} + \frac{51}{80}e^{5} - \frac{153}{80}e^{3} - \frac{51}{20}e$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{1}{32}e^{9} + \frac{21}{32}e^{7} + \frac{131}{32}e^{5} + \frac{267}{32}e^{3} + \frac{47}{8}e$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{3}{32}e^{9} - \frac{63}{32}e^{7} - \frac{385}{32}e^{5} - \frac{697}{32}e^{3} - \frac{85}{8}e$ |
| 11 | $[11, 11, w + 10]$ | $\phantom{-}\frac{1}{80}e^{9} + \frac{3}{20}e^{7} - \frac{39}{80}e^{5} - \frac{269}{40}e^{3} - \frac{43}{10}e$ |
| 17 | $[17, 17, -3w + 17]$ | $\phantom{-}\frac{1}{16}e^{8} + \frac{5}{4}e^{6} + \frac{109}{16}e^{4} + \frac{65}{8}e^{2} + \frac{3}{2}$ |
| 29 | $[29, 29, w + 11]$ | $\phantom{-}\frac{1}{10}e^{9} + \frac{171}{80}e^{7} + \frac{539}{40}e^{5} + \frac{2031}{80}e^{3} + \frac{127}{20}e$ |
| 29 | $[29, 29, w + 18]$ | $-\frac{3}{160}e^{9} - \frac{91}{160}e^{7} - \frac{913}{160}e^{5} - \frac{3261}{160}e^{3} - \frac{577}{40}e$ |
| 37 | $[37, 37, w + 16]$ | $\phantom{-}\frac{3}{80}e^{9} + \frac{7}{10}e^{7} + \frac{243}{80}e^{5} - \frac{37}{40}e^{3} - \frac{59}{10}e$ |
| 37 | $[37, 37, w + 21]$ | $-\frac{27}{160}e^{9} - \frac{559}{160}e^{7} - \frac{3337}{160}e^{5} - \frac{5929}{160}e^{3} - \frac{973}{40}e$ |
| 47 | $[47, 47, -w - 9]$ | $-\frac{1}{4}e^{8} - \frac{43}{8}e^{6} - \frac{139}{4}e^{4} - \frac{577}{8}e^{2} - \frac{77}{2}$ |
| 47 | $[47, 47, w - 9]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{11}{2}e^{6} + \frac{73}{2}e^{4} + \frac{309}{4}e^{2} + 39$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{4}e^{8} + 5e^{6} + \frac{109}{4}e^{4} + \frac{67}{2}e^{2} + 6$ |
| 61 | $[61, 61, w + 20]$ | $-\frac{1}{20}e^{9} - \frac{83}{80}e^{7} - \frac{247}{40}e^{5} - \frac{843}{80}e^{3} - \frac{171}{20}e$ |
| 61 | $[61, 61, w + 41]$ | $\phantom{-}\frac{19}{160}e^{9} + \frac{433}{160}e^{7} + \frac{3069}{160}e^{5} + \frac{7323}{160}e^{3} + \frac{991}{40}e$ |
| 89 | $[89, 89, 2w - 15]$ | $-\frac{1}{16}e^{8} - \frac{5}{4}e^{6} - \frac{101}{16}e^{4} - \frac{5}{8}e^{2} + \frac{33}{2}$ |
| 89 | $[89, 89, -2w - 15]$ | $\phantom{-}\frac{1}{16}e^{8} + \frac{13}{8}e^{6} + \frac{225}{16}e^{4} + \frac{91}{2}e^{2} + 31$ |
| 103 | $[103, 103, -14w + 81]$ | $-\frac{5}{16}e^{8} - \frac{47}{8}e^{6} - \frac{429}{16}e^{4} - \frac{33}{4}e^{2} + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 6]$ | $-1$ |
| $5$ | $[5, 5, w + 2]$ | $-\frac{1}{80}e^{9} - \frac{17}{80}e^{7} - \frac{51}{80}e^{5} + \frac{153}{80}e^{3} + \frac{51}{20}e$ |