Base field \(\Q(\sqrt{5}, \sqrt{7})\)
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 15x^{2} + 16x + 29\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19,19,\frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ |
Dimension: | $20$ |
CM: | no |
Base change: | no |
Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{20} + 4x^{19} - 33x^{18} - 130x^{17} + 447x^{16} + 1669x^{15} - 3326x^{14} - 10888x^{13} + 15487x^{12} + 38604x^{11} - 47385x^{10} - 71872x^{9} + 91709x^{8} + 56127x^{7} - 97476x^{6} + 5121x^{5} + 39385x^{4} - 20842x^{3} + 3795x^{2} - 92x - 28\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{1}{23}]$ | $\phantom{-}e$ |
9 | $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$ | $...$ |
9 | $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{68}{23}]$ | $...$ |
19 | $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{24}{23}]$ | $...$ |
19 | $[19, 19, -\frac{6}{23}w^{3} + \frac{9}{23}w^{2} + \frac{83}{23}w - \frac{20}{23}]$ | $...$ |
19 | $[19, 19, \frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ | $-1$ |
19 | $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w - \frac{22}{23}]$ | $...$ |
25 | $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ | $...$ |
29 | $[29, 29, w]$ | $...$ |
29 | $[29, 29, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w - \frac{21}{23}]$ | $...$ |
29 | $[29, 29, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{44}{23}]$ | $...$ |
29 | $[29, 29, -w + 1]$ | $...$ |
31 | $[31, 31, w + 2]$ | $...$ |
31 | $[31, 31, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w + \frac{25}{23}]$ | $...$ |
31 | $[31, 31, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{90}{23}]$ | $...$ |
31 | $[31, 31, -w + 3]$ | $...$ |
49 | $[49, 7, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{22}{23}]$ | $...$ |
59 | $[59, 59, -\frac{20}{23}w^{3} + \frac{30}{23}w^{2} + \frac{269}{23}w - \frac{128}{23}]$ | $...$ |
59 | $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{88}{23}]$ | $...$ |
59 | $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{19}{23}]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19,19,\frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ | $1$ |