Base field \(\Q(\sqrt{205}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9,9,w + 6]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 19x^{8} + 123x^{6} + 301x^{4} + 196x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{1}{12}e^{8} - \frac{7}{6}e^{6} - \frac{59}{12}e^{4} - \frac{13}{2}e^{2} - \frac{7}{3}$ |
| 5 | $[5, 5, -w + 8]$ | $\phantom{-}\frac{1}{12}e^{8} + \frac{7}{6}e^{6} + \frac{59}{12}e^{4} + \frac{11}{2}e^{2} - \frac{2}{3}$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{1}{12}e^{9} + \frac{5}{3}e^{7} + \frac{137}{12}e^{5} + \frac{59}{2}e^{3} + \frac{58}{3}e$ |
| 7 | $[7, 7, w + 5]$ | $\phantom{-}\frac{1}{12}e^{9} + \frac{5}{3}e^{7} + \frac{131}{12}e^{5} + 25e^{3} + \frac{37}{3}e$ |
| 13 | $[13, 13, w + 3]$ | $-\frac{1}{12}e^{9} - \frac{17}{12}e^{7} - \frac{101}{12}e^{5} - \frac{79}{4}e^{3} - \frac{34}{3}e$ |
| 13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{1}{6}e^{9} + \frac{37}{12}e^{7} + \frac{113}{6}e^{5} + \frac{161}{4}e^{3} + \frac{50}{3}e$ |
| 17 | $[17, 17, w]$ | $\phantom{-}\frac{1}{6}e^{9} + \frac{37}{12}e^{7} + \frac{119}{6}e^{5} + \frac{201}{4}e^{3} + \frac{113}{3}e$ |
| 17 | $[17, 17, w + 16]$ | $\phantom{-}\frac{1}{6}e^{9} + \frac{31}{12}e^{7} + \frac{77}{6}e^{5} + \frac{83}{4}e^{3} + \frac{8}{3}e$ |
| 31 | $[31, 31, -w - 4]$ | $\phantom{-}\frac{1}{12}e^{8} + \frac{5}{3}e^{6} + \frac{131}{12}e^{4} + 25e^{2} + \frac{34}{3}$ |
| 31 | $[31, 31, w - 5]$ | $-\frac{1}{6}e^{8} - \frac{11}{6}e^{6} - \frac{16}{3}e^{4} - 5e^{2} - \frac{14}{3}$ |
| 41 | $[41, 41, 3w - 22]$ | $\phantom{-}\frac{1}{4}e^{8} + 4e^{6} + \frac{81}{4}e^{4} + \frac{67}{2}e^{2} + 8$ |
| 47 | $[47, 47, w + 19]$ | $\phantom{-}\frac{1}{4}e^{9} + 4e^{7} + \frac{89}{4}e^{5} + \frac{103}{2}e^{3} + 41e$ |
| 47 | $[47, 47, w + 27]$ | $\phantom{-}2e^{3} + 12e$ |
| 53 | $[53, 53, w + 14]$ | $-\frac{1}{4}e^{9} - \frac{19}{4}e^{7} - \frac{123}{4}e^{5} - \frac{301}{4}e^{3} - 49e$ |
| 53 | $[53, 53, w + 38]$ | $\phantom{-}\frac{1}{4}e^{9} + \frac{21}{4}e^{7} + \frac{147}{4}e^{5} + \frac{371}{4}e^{3} + 50e$ |
| 59 | $[59, 59, -w - 10]$ | $-\frac{1}{3}e^{8} - \frac{14}{3}e^{6} - \frac{62}{3}e^{4} - 31e^{2} - \frac{16}{3}$ |
| 59 | $[59, 59, w - 11]$ | $-\frac{1}{12}e^{8} - \frac{7}{6}e^{6} - \frac{53}{12}e^{4} - 4e^{2} - \frac{4}{3}$ |
| 61 | $[61, 61, 2w - 13]$ | $-\frac{1}{6}e^{8} - \frac{7}{3}e^{6} - \frac{31}{3}e^{4} - \frac{31}{2}e^{2} - \frac{2}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 3]$ | $-1$ |