Base field \(\Q(\sqrt{109}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 27\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[20, 10, -6w + 34]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 2x^{6} - 11x^{5} - 12x^{4} + 39x^{3} + 8x^{2} - 36x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}\frac{1}{4}e^{6} + e^{5} - \frac{5}{4}e^{4} - \frac{13}{2}e^{3} + \frac{3}{4}e^{2} + 8e + 1$ |
| 3 | $[3, 3, w + 5]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 5 | $[5, 5, -3w + 17]$ | $-1$ |
| 5 | $[5, 5, -3w - 14]$ | $-\frac{1}{2}e^{6} - \frac{3}{2}e^{5} + 4e^{4} + 10e^{3} - 10e^{2} - \frac{27}{2}e + 7$ |
| 7 | $[7, 7, w - 5]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{3}{2}e^{5} - \frac{7}{2}e^{4} - 9e^{3} + 6e^{2} + 10e$ |
| 7 | $[7, 7, w + 4]$ | $-\frac{1}{4}e^{6} - \frac{1}{2}e^{5} + \frac{11}{4}e^{4} + \frac{7}{2}e^{3} - \frac{33}{4}e^{2} - \frac{9}{2}e + 3$ |
| 29 | $[29, 29, -w - 7]$ | $-e^{3} - e^{2} + 6e + 2$ |
| 29 | $[29, 29, -w + 8]$ | $\phantom{-}\frac{3}{2}e^{6} + \frac{9}{2}e^{5} - \frac{23}{2}e^{4} - 28e^{3} + 28e^{2} + 32e - 20$ |
| 31 | $[31, 31, -5w + 28]$ | $\phantom{-}\frac{3}{4}e^{6} + \frac{5}{2}e^{5} - \frac{19}{4}e^{4} - \frac{29}{2}e^{3} + \frac{35}{4}e^{2} + 11e - 3$ |
| 31 | $[31, 31, -5w - 23]$ | $-\frac{1}{4}e^{6} + \frac{17}{4}e^{4} + e^{3} - \frac{57}{4}e^{2} - \frac{3}{2}e + 5$ |
| 43 | $[43, 43, 6w + 29]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{3}{2}e^{5} - \frac{5}{2}e^{4} - \frac{13}{2}e^{3} + \frac{1}{2}e^{2} + \frac{3}{2}e + 7$ |
| 43 | $[43, 43, -6w + 35]$ | $-\frac{1}{2}e^{6} - 2e^{5} + \frac{5}{2}e^{4} + 13e^{3} - \frac{7}{2}e^{2} - 17e + 6$ |
| 61 | $[61, 61, 3w - 19]$ | $-\frac{1}{2}e^{6} - e^{5} + \frac{11}{2}e^{4} + \frac{13}{2}e^{3} - 16e^{2} - \frac{9}{2}e + 7$ |
| 61 | $[61, 61, -3w - 16]$ | $\phantom{-}\frac{1}{4}e^{6} + e^{5} - \frac{9}{4}e^{4} - 8e^{3} + \frac{41}{4}e^{2} + \frac{33}{2}e - 11$ |
| 71 | $[71, 71, -7w - 34]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{3}{2}e^{4} - \frac{7}{2}e^{3} - 7e^{2} + 10e + 2$ |
| 71 | $[71, 71, 7w - 41]$ | $\phantom{-}2e^{6} + 6e^{5} - \frac{31}{2}e^{4} - \frac{77}{2}e^{3} + \frac{73}{2}e^{2} + 49e - 24$ |
| 73 | $[73, 73, 2w - 7]$ | $\phantom{-}2e^{6} + \frac{13}{2}e^{5} - 14e^{4} - 40e^{3} + \frac{61}{2}e^{2} + 43e - 16$ |
| 73 | $[73, 73, -2w - 5]$ | $-\frac{5}{4}e^{6} - \frac{7}{2}e^{5} + \frac{41}{4}e^{4} + 20e^{3} - \frac{115}{4}e^{2} - \frac{31}{2}e + 19$ |
| 83 | $[83, 83, -w - 10]$ | $-\frac{1}{2}e^{6} - \frac{3}{2}e^{5} + \frac{7}{2}e^{4} + 9e^{3} - 6e^{2} - 6e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |
| $5$ | $[5, 5, -3w + 17]$ | $1$ |