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: | $[9, 9, -w + 7]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 2x^{5} - 4x^{4} + 2x^{3} + 23x^{2} + 20x + 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-\frac{2}{53}e^{5} + \frac{21}{265}e^{4} + \frac{22}{265}e^{3} - \frac{1}{265}e^{2} - \frac{267}{265}e - \frac{23}{53}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}0$ |
| 4 | $[4, 2, 2]$ | $-\frac{2}{53}e^{5} + \frac{21}{265}e^{4} + \frac{22}{265}e^{3} - \frac{1}{265}e^{2} - \frac{2}{265}e - \frac{23}{53}$ |
| 5 | $[5, 5, -w + 8]$ | $-\frac{34}{265}e^{5} + \frac{27}{53}e^{4} - \frac{2}{53}e^{3} - \frac{77}{53}e^{2} - \frac{346}{265}e + \frac{49}{53}$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{9}{265}e^{5} - \frac{3}{265}e^{4} - \frac{41}{265}e^{3} + \frac{38}{265}e^{2} + \frac{182}{265}e + \frac{26}{53}$ |
| 7 | $[7, 7, w + 5]$ | $\phantom{-}\frac{1}{265}e^{5} + \frac{7}{53}e^{4} - \frac{28}{53}e^{3} + \frac{35}{53}e^{2} - \frac{21}{265}e + \frac{50}{53}$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{21}{265}e^{5} - \frac{12}{53}e^{4} - \frac{5}{53}e^{3} - \frac{7}{53}e^{2} + \frac{619}{265}e + \frac{43}{53}$ |
| 13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{44}{265}e^{5} - \frac{103}{265}e^{4} - \frac{171}{265}e^{3} + \frac{68}{265}e^{2} + \frac{1302}{265}e + \frac{133}{53}$ |
| 17 | $[17, 17, w]$ | $\phantom{-}\frac{1}{53}e^{5} + \frac{16}{265}e^{4} - \frac{223}{265}e^{3} + \frac{239}{265}e^{2} + \frac{213}{265}e + \frac{91}{53}$ |
| 17 | $[17, 17, w + 16]$ | $-\frac{9}{53}e^{5} + \frac{68}{265}e^{4} + \frac{311}{265}e^{3} - \frac{243}{265}e^{2} - \frac{1281}{265}e - \frac{183}{53}$ |
| 31 | $[31, 31, -w - 4]$ | $-\frac{14}{53}e^{5} + \frac{306}{265}e^{4} - \frac{58}{265}e^{3} - \frac{961}{265}e^{2} - \frac{862}{265}e + \frac{104}{53}$ |
| 31 | $[31, 31, w - 5]$ | $-\frac{2}{53}e^{5} + \frac{21}{265}e^{4} + \frac{22}{265}e^{3} - \frac{1}{265}e^{2} - \frac{2}{265}e + \frac{189}{53}$ |
| 41 | $[41, 41, 3w - 22]$ | $-\frac{8}{265}e^{5} - \frac{3}{53}e^{4} + \frac{12}{53}e^{3} + \frac{38}{53}e^{2} + \frac{168}{265}e + \frac{183}{53}$ |
| 47 | $[47, 47, w + 19]$ | $\phantom{-}\frac{2}{265}e^{5} - \frac{36}{265}e^{4} + \frac{38}{265}e^{3} - \frac{74}{265}e^{2} + \frac{34}{53}e - \frac{6}{53}$ |
| 47 | $[47, 47, w + 27]$ | $\phantom{-}\frac{17}{265}e^{5} - \frac{94}{265}e^{4} - \frac{48}{265}e^{3} - \frac{46}{265}e^{2} + \frac{756}{265}e + \frac{55}{53}$ |
| 53 | $[53, 53, w + 14]$ | $\phantom{-}\frac{2}{53}e^{5} - \frac{21}{265}e^{4} - \frac{22}{265}e^{3} + \frac{1}{265}e^{2} + \frac{267}{265}e + \frac{23}{53}$ |
| 53 | $[53, 53, w + 38]$ | $-\frac{14}{53}e^{5} + \frac{40}{53}e^{4} + \frac{52}{53}e^{3} - \frac{12}{53}e^{2} - \frac{448}{53}e - \frac{214}{53}$ |
| 59 | $[59, 59, -w - 10]$ | $-\frac{28}{265}e^{5} + \frac{27}{265}e^{4} + \frac{104}{265}e^{3} + \frac{188}{265}e^{2} + \frac{164}{265}e - \frac{22}{53}$ |
| 59 | $[59, 59, w - 11]$ | $\phantom{-}\frac{88}{265}e^{5} - \frac{312}{265}e^{4} - \frac{24}{265}e^{3} + \frac{772}{265}e^{2} + \frac{696}{265}e - \frac{158}{53}$ |
| 61 | $[61, 61, 2w - 13]$ | $\phantom{-}\frac{6}{265}e^{5} - \frac{108}{265}e^{4} + \frac{114}{265}e^{3} + \frac{573}{265}e^{2} + \frac{102}{53}e - \frac{283}{53}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 2]$ | $1$ |