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: | $[7,7,-w - 4]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 2x^{5} - 17x^{4} + 30x^{3} + 81x^{2} - 87x - 143\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 5]$ | $-\frac{1}{5}e^{5} + \frac{17}{5}e^{3} + \frac{4}{5}e^{2} - \frac{68}{5}e - \frac{44}{5}$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{8}{5}e^{5} + e^{4} - \frac{121}{5}e^{3} - \frac{77}{5}e^{2} + \frac{414}{5}e + \frac{402}{5}$ |
| 5 | $[5, 5, -3w + 17]$ | $\phantom{-}\frac{3}{5}e^{5} - \frac{46}{5}e^{3} - \frac{7}{5}e^{2} + \frac{154}{5}e + \frac{112}{5}$ |
| 5 | $[5, 5, -3w - 14]$ | $\phantom{-}\frac{9}{5}e^{5} + e^{4} - \frac{133}{5}e^{3} - \frac{76}{5}e^{2} + \frac{442}{5}e + \frac{406}{5}$ |
| 7 | $[7, 7, w - 5]$ | $\phantom{-}\frac{7}{5}e^{5} + e^{4} - \frac{104}{5}e^{3} - \frac{73}{5}e^{2} + \frac{346}{5}e + \frac{353}{5}$ |
| 7 | $[7, 7, w + 4]$ | $-1$ |
| 29 | $[29, 29, -w - 7]$ | $\phantom{-}\frac{7}{5}e^{5} + 2e^{4} - \frac{104}{5}e^{3} - \frac{138}{5}e^{2} + \frac{361}{5}e + \frac{503}{5}$ |
| 29 | $[29, 29, -w + 8]$ | $\phantom{-}3e^{5} + 2e^{4} - 45e^{3} - 31e^{2} + 152e + 159$ |
| 31 | $[31, 31, -5w + 28]$ | $-\frac{1}{5}e^{5} + \frac{17}{5}e^{3} + \frac{9}{5}e^{2} - \frac{63}{5}e - \frac{84}{5}$ |
| 31 | $[31, 31, -5w - 23]$ | $-3e^{5} - 3e^{4} + 44e^{3} + 41e^{2} - 148e - 166$ |
| 43 | $[43, 43, 6w + 29]$ | $-\frac{9}{5}e^{5} - e^{4} + \frac{143}{5}e^{3} + \frac{101}{5}e^{2} - \frac{527}{5}e - \frac{566}{5}$ |
| 43 | $[43, 43, -6w + 35]$ | $\phantom{-}e^{4} - 2e^{3} - 15e^{2} + 20e + 48$ |
| 61 | $[61, 61, 3w - 19]$ | $-\frac{27}{5}e^{5} - 4e^{4} + \frac{409}{5}e^{3} + \frac{308}{5}e^{2} - \frac{1421}{5}e - \frac{1503}{5}$ |
| 61 | $[61, 61, -3w - 16]$ | $-\frac{17}{5}e^{5} - e^{4} + \frac{254}{5}e^{3} + \frac{93}{5}e^{2} - \frac{836}{5}e - \frac{683}{5}$ |
| 71 | $[71, 71, -7w - 34]$ | $\phantom{-}7e^{5} + 4e^{4} - 104e^{3} - 62e^{2} + 349e + 333$ |
| 71 | $[71, 71, 7w - 41]$ | $-\frac{23}{5}e^{5} - e^{4} + \frac{346}{5}e^{3} + \frac{112}{5}e^{2} - \frac{1149}{5}e - \frac{917}{5}$ |
| 73 | $[73, 73, 2w - 7]$ | $\phantom{-}\frac{7}{5}e^{5} + 2e^{4} - \frac{104}{5}e^{3} - \frac{138}{5}e^{2} + \frac{351}{5}e + \frac{488}{5}$ |
| 73 | $[73, 73, -2w - 5]$ | $\phantom{-}\frac{17}{5}e^{5} + 2e^{4} - \frac{259}{5}e^{3} - \frac{163}{5}e^{2} + \frac{896}{5}e + \frac{868}{5}$ |
| 83 | $[83, 83, -w - 10]$ | $\phantom{-}\frac{4}{5}e^{5} - \frac{53}{5}e^{3} + \frac{4}{5}e^{2} + \frac{132}{5}e + \frac{81}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,-w - 4]$ | $1$ |