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: | $[12,6,-2w + 2]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $68$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 6x^{6} + 7x^{5} + 16x^{4} - 33x^{3} + 4x^{2} + 13x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 5 | $[5, 5, -w + 8]$ | $\phantom{-}\frac{3}{5}e^{6} - \frac{11}{5}e^{5} - \frac{8}{5}e^{4} + \frac{46}{5}e^{3} - \frac{38}{5}e - \frac{3}{5}$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{2}{5}e^{6} + \frac{14}{5}e^{5} - \frac{18}{5}e^{4} - \frac{44}{5}e^{3} + 15e^{2} + \frac{17}{5}e - \frac{18}{5}$ |
| 7 | $[7, 7, w + 5]$ | $\phantom{-}\frac{4}{5}e^{6} - \frac{18}{5}e^{5} + \frac{1}{5}e^{4} + \frac{63}{5}e^{3} - 6e^{2} - \frac{29}{5}e + \frac{1}{5}$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{6}{5}e^{6} - \frac{22}{5}e^{5} - \frac{11}{5}e^{4} + \frac{72}{5}e^{3} - e^{2} - \frac{21}{5}e - \frac{11}{5}$ |
| 13 | $[13, 13, w + 9]$ | $-e^{6} + 5e^{5} - 3e^{4} - 14e^{3} + 16e^{2} - e - 1$ |
| 17 | $[17, 17, w]$ | $\phantom{-}\frac{1}{5}e^{6} - \frac{7}{5}e^{5} + \frac{19}{5}e^{4} - \frac{3}{5}e^{3} - 16e^{2} + \frac{69}{5}e + \frac{34}{5}$ |
| 17 | $[17, 17, w + 16]$ | $\phantom{-}\frac{6}{5}e^{6} - \frac{27}{5}e^{5} - \frac{1}{5}e^{4} + \frac{107}{5}e^{3} - 9e^{2} - \frac{81}{5}e + \frac{9}{5}$ |
| 31 | $[31, 31, -w - 4]$ | $\phantom{-}\frac{8}{5}e^{6} - \frac{31}{5}e^{5} - \frac{8}{5}e^{4} + \frac{101}{5}e^{3} - 8e^{2} - \frac{28}{5}e + \frac{12}{5}$ |
| 31 | $[31, 31, w - 5]$ | $\phantom{-}e^{6} - 5e^{5} + 3e^{4} + 15e^{3} - 20e^{2} + 2e + 6$ |
| 41 | $[41, 41, 3w - 22]$ | $-\frac{4}{5}e^{6} + \frac{28}{5}e^{5} - \frac{41}{5}e^{4} - \frac{78}{5}e^{3} + 35e^{2} - \frac{1}{5}e - \frac{61}{5}$ |
| 47 | $[47, 47, w + 19]$ | $\phantom{-}\frac{3}{5}e^{6} - \frac{11}{5}e^{5} - \frac{13}{5}e^{4} + \frac{66}{5}e^{3} + e^{2} - \frac{103}{5}e + \frac{7}{5}$ |
| 47 | $[47, 47, w + 27]$ | $\phantom{-}\frac{11}{5}e^{6} - \frac{52}{5}e^{5} + \frac{14}{5}e^{4} + \frac{182}{5}e^{3} - 28e^{2} - \frac{76}{5}e + \frac{39}{5}$ |
| 53 | $[53, 53, w + 14]$ | $-2e^{6} + 10e^{5} - 5e^{4} - 32e^{3} + 35e^{2} + 3e - 13$ |
| 53 | $[53, 53, w + 38]$ | $-e^{6} + 3e^{5} + 5e^{4} - 14e^{3} - 7e^{2} + 13e + 1$ |
| 59 | $[59, 59, -w - 10]$ | $-\frac{8}{5}e^{6} + \frac{36}{5}e^{5} - \frac{7}{5}e^{4} - \frac{131}{5}e^{3} + 24e^{2} + \frac{73}{5}e - \frac{67}{5}$ |
| 59 | $[59, 59, w - 11]$ | $-e^{6} + 6e^{5} - 5e^{4} - 20e^{3} + 23e^{2} + 6e - 5$ |
| 61 | $[61, 61, 2w - 13]$ | $\phantom{-}\frac{8}{5}e^{6} - \frac{36}{5}e^{5} - \frac{3}{5}e^{4} + \frac{146}{5}e^{3} - 13e^{2} - \frac{103}{5}e + \frac{47}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 1]$ | $1$ |
| $4$ | $[4,2,2]$ | $1$ |