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: | $[15,15,-w + 7]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - x^{4} - 10x^{3} + 4x^{2} + 11x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 5]$ | $\phantom{-}1$ |
| 4 | $[4, 2, 2]$ | $-e$ |
| 5 | $[5, 5, -3w + 17]$ | $-\frac{2}{5}e^{4} + \frac{3}{5}e^{3} + \frac{16}{5}e^{2} - \frac{16}{5}e - \frac{4}{5}$ |
| 5 | $[5, 5, -3w - 14]$ | $-1$ |
| 7 | $[7, 7, w - 5]$ | $\phantom{-}\frac{1}{5}e^{4} - \frac{4}{5}e^{3} - \frac{8}{5}e^{2} + \frac{28}{5}e + \frac{2}{5}$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{3}{5}e^{4} - \frac{2}{5}e^{3} - \frac{29}{5}e^{2} + \frac{4}{5}e + \frac{16}{5}$ |
| 29 | $[29, 29, -w - 7]$ | $-\frac{6}{5}e^{4} + \frac{9}{5}e^{3} + \frac{58}{5}e^{2} - \frac{53}{5}e - \frac{32}{5}$ |
| 29 | $[29, 29, -w + 8]$ | $-\frac{4}{5}e^{4} + \frac{6}{5}e^{3} + \frac{32}{5}e^{2} - \frac{32}{5}e - \frac{23}{5}$ |
| 31 | $[31, 31, -5w + 28]$ | $-\frac{3}{5}e^{4} + \frac{2}{5}e^{3} + \frac{34}{5}e^{2} - \frac{9}{5}e - \frac{41}{5}$ |
| 31 | $[31, 31, -5w - 23]$ | $\phantom{-}\frac{2}{5}e^{4} - \frac{3}{5}e^{3} - \frac{16}{5}e^{2} + \frac{21}{5}e - \frac{6}{5}$ |
| 43 | $[43, 43, 6w + 29]$ | $\phantom{-}\frac{4}{5}e^{4} - \frac{6}{5}e^{3} - \frac{42}{5}e^{2} + \frac{32}{5}e + \frac{28}{5}$ |
| 43 | $[43, 43, -6w + 35]$ | $\phantom{-}\frac{2}{5}e^{4} - \frac{3}{5}e^{3} - \frac{16}{5}e^{2} + \frac{21}{5}e - \frac{36}{5}$ |
| 61 | $[61, 61, 3w - 19]$ | $-\frac{3}{5}e^{4} + \frac{2}{5}e^{3} + \frac{24}{5}e^{2} - \frac{4}{5}e - \frac{21}{5}$ |
| 61 | $[61, 61, -3w - 16]$ | $\phantom{-}\frac{8}{5}e^{4} - \frac{12}{5}e^{3} - \frac{69}{5}e^{2} + \frac{54}{5}e + \frac{26}{5}$ |
| 71 | $[71, 71, -7w - 34]$ | $\phantom{-}\frac{11}{5}e^{4} - \frac{9}{5}e^{3} - \frac{108}{5}e^{2} + \frac{23}{5}e + \frac{77}{5}$ |
| 71 | $[71, 71, 7w - 41]$ | $-\frac{6}{5}e^{4} + \frac{4}{5}e^{3} + \frac{63}{5}e^{2} - \frac{28}{5}e - \frac{72}{5}$ |
| 73 | $[73, 73, 2w - 7]$ | $\phantom{-}e^{4} - e^{3} - 10e^{2} + 7e + 5$ |
| 73 | $[73, 73, -2w - 5]$ | $-\frac{4}{5}e^{4} + \frac{11}{5}e^{3} + \frac{32}{5}e^{2} - \frac{77}{5}e - \frac{48}{5}$ |
| 83 | $[83, 83, -w - 10]$ | $\phantom{-}3e^{4} - 3e^{3} - 28e^{2} + 11e + 17$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,w + 5]$ | $-1$ |
| $5$ | $[5,5,3w + 14]$ | $1$ |