Base field \(\Q(\sqrt{429}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 107\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[1, 1, 1]$ |
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:
\(x^{8} + 72x^{6} + 1300x^{4} + 3024x^{2} + 1156\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 11]$ | $-\frac{1}{342}e^{6} - \frac{37}{171}e^{4} - \frac{667}{171}e^{2} - \frac{794}{171}$ |
4 | $[4, 2, 2]$ | $-\frac{1}{684}e^{6} - \frac{37}{342}e^{4} - \frac{667}{342}e^{2} - \frac{226}{171}$ |
5 | $[5, 5, w + 1]$ | $-\frac{37}{23256}e^{7} - \frac{2681}{23256}e^{5} - \frac{24679}{11628}e^{3} - \frac{73097}{11628}e$ |
5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{37}{23256}e^{7} + \frac{2681}{23256}e^{5} + \frac{24679}{11628}e^{3} + \frac{73097}{11628}e$ |
7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{37}{23256}e^{7} + \frac{2681}{23256}e^{5} + \frac{24679}{11628}e^{3} + \frac{61469}{11628}e$ |
7 | $[7, 7, w + 5]$ | $-\frac{37}{23256}e^{7} - \frac{2681}{23256}e^{5} - \frac{24679}{11628}e^{3} - \frac{61469}{11628}e$ |
11 | $[11, 11, w + 5]$ | $\phantom{-}0$ |
13 | $[13, 13, w + 6]$ | $\phantom{-}0$ |
17 | $[17, 17, w - 10]$ | $-\frac{5}{684}e^{6} - \frac{683}{1368}e^{4} - \frac{1411}{171}e^{2} - \frac{7883}{684}$ |
17 | $[17, 17, w + 9]$ | $-\frac{5}{684}e^{6} - \frac{683}{1368}e^{4} - \frac{1411}{171}e^{2} - \frac{7883}{684}$ |
19 | $[19, 19, w + 3]$ | $-\frac{11}{3876}e^{7} - \frac{511}{2584}e^{5} - \frac{3184}{969}e^{3} - \frac{4271}{1292}e$ |
19 | $[19, 19, w + 15]$ | $\phantom{-}\frac{11}{3876}e^{7} + \frac{511}{2584}e^{5} + \frac{3184}{969}e^{3} + \frac{4271}{1292}e$ |
29 | $[29, 29, -2w + 21]$ | $\phantom{-}\frac{7}{1368}e^{6} + \frac{461}{1368}e^{4} + \frac{3301}{684}e^{2} - \frac{655}{684}$ |
29 | $[29, 29, 5w - 54]$ | $\phantom{-}\frac{7}{1368}e^{6} + \frac{461}{1368}e^{4} + \frac{3301}{684}e^{2} - \frac{655}{684}$ |
47 | $[47, 47, w + 18]$ | $\phantom{-}\frac{137}{23256}e^{7} + \frac{2449}{5814}e^{5} + \frac{85565}{11628}e^{3} + \frac{31726}{2907}e$ |
47 | $[47, 47, w + 28]$ | $-\frac{137}{23256}e^{7} - \frac{2449}{5814}e^{5} - \frac{85565}{11628}e^{3} - \frac{31726}{2907}e$ |
59 | $[59, 59, w + 27]$ | $\phantom{-}\frac{37}{11628}e^{7} + \frac{2681}{11628}e^{5} + \frac{24679}{5814}e^{3} + \frac{73097}{5814}e$ |
59 | $[59, 59, w + 31]$ | $-\frac{37}{11628}e^{7} - \frac{2681}{11628}e^{5} - \frac{24679}{5814}e^{3} - \frac{73097}{5814}e$ |
71 | $[71, 71, w + 21]$ | $-\frac{211}{23256}e^{7} - \frac{7579}{11628}e^{5} - \frac{134923}{11628}e^{3} - \frac{136549}{5814}e$ |
71 | $[71, 71, w + 49]$ | $\phantom{-}\frac{211}{23256}e^{7} + \frac{7579}{11628}e^{5} + \frac{134923}{11628}e^{3} + \frac{136549}{5814}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).