Base field \(\Q(\sqrt{42}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 42\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w - 7]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 90x^{6} + 1697x^{4} + 11700x^{2} + 26896\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{3}{328}e^{7} + \frac{91}{123}e^{5} + \frac{2877}{328}e^{3} + \frac{3220}{123}e$ |
| 3 | $[3, 3, w]$ | $-\frac{39}{2296}e^{7} - \frac{1591}{1148}e^{5} - \frac{39451}{2296}e^{3} - \frac{15935}{287}e$ |
| 7 | $[7, 7, w - 7]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w + 3]$ | $-\frac{39}{2296}e^{7} - \frac{1591}{1148}e^{5} - \frac{39451}{2296}e^{3} - \frac{15648}{287}e$ |
| 11 | $[11, 11, w + 8]$ | $-\frac{3}{287}e^{7} - \frac{957}{1148}e^{5} - \frac{10483}{1148}e^{3} - \frac{6892}{287}e$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{5}{574}e^{7} + \frac{409}{574}e^{5} + \frac{2582}{287}e^{3} + \frac{9160}{287}e$ |
| 13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{19}{2296}e^{7} + \frac{773}{1148}e^{5} + \frac{2685}{328}e^{3} + \frac{6775}{287}e$ |
| 17 | $[17, 17, -w - 5]$ | $\phantom{-}\frac{1}{21}e^{6} + \frac{82}{21}e^{4} + \frac{1039}{21}e^{2} + \frac{3382}{21}$ |
| 17 | $[17, 17, -w + 5]$ | $-\frac{1}{42}e^{6} - \frac{79}{42}e^{4} - \frac{410}{21}e^{2} - \frac{992}{21}$ |
| 19 | $[19, 19, w + 2]$ | $\phantom{-}\frac{29}{3444}e^{7} + \frac{197}{287}e^{5} + \frac{29123}{3444}e^{3} + \frac{7570}{287}e$ |
| 19 | $[19, 19, w + 17]$ | $\phantom{-}\frac{59}{6888}e^{7} + \frac{803}{1148}e^{5} + \frac{60107}{6888}e^{3} + \frac{1195}{41}e$ |
| 25 | $[25, 5, 5]$ | $-2$ |
| 29 | $[29, 29, w + 10]$ | $\phantom{-}\frac{81}{2296}e^{7} + \frac{9869}{3444}e^{5} + \frac{79729}{2296}e^{3} + \frac{92024}{861}e$ |
| 29 | $[29, 29, w + 19]$ | $\phantom{-}\frac{33}{1148}e^{7} + \frac{7967}{3444}e^{5} + \frac{15311}{574}e^{3} + \frac{65756}{861}e$ |
| 41 | $[41, 41, -w - 1]$ | $\phantom{-}\frac{1}{28}e^{6} + \frac{83}{28}e^{4} + \frac{278}{7}e^{2} + \frac{962}{7}$ |
| 41 | $[41, 41, w - 1]$ | $\phantom{-}\frac{1}{14}e^{4} + \frac{73}{14}e^{2} + \frac{233}{7}$ |
| 47 | $[47, 47, -2w + 11]$ | $-\frac{1}{14}e^{6} - \frac{81}{14}e^{4} - 69e^{2} - \frac{1458}{7}$ |
| 47 | $[47, 47, 4w - 25]$ | $\phantom{-}\frac{1}{14}e^{6} + \frac{81}{14}e^{4} + 69e^{2} + \frac{1458}{7}$ |
| 53 | $[53, 53, w + 25]$ | $\phantom{-}\frac{3}{2296}e^{7} + \frac{323}{3444}e^{5} + \frac{827}{2296}e^{3} - \frac{1864}{861}e$ |
| 53 | $[53, 53, w + 28]$ | $\phantom{-}\frac{9}{1148}e^{7} + \frac{2225}{3444}e^{5} + \frac{2414}{287}e^{3} + \frac{24404}{861}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w - 7]$ | $-1$ |