Base field \(\Q(\sqrt{449}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 112\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[8, 8, 443w + 4472]$ |
Dimension: | $42$ |
CM: | no |
Base change: | no |
Newspace dimension: | $79$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{42} + x^{41} - 65x^{40} - 60x^{39} + 1941x^{38} + 1634x^{37} - 35312x^{36} - 26707x^{35} + 437636x^{34} + 291769x^{33} - 3914158x^{32} - 2243989x^{31} + 26111129x^{30} + 12445917x^{29} - 132436660x^{28} - 49989381x^{27} + 515975112x^{26} + 142731177x^{25} - 1549734082x^{24} - 271522935x^{23} + 3581474676x^{22} + 266264317x^{21} - 6323197365x^{20} + 157152208x^{19} + 8420368802x^{18} - 1022830817x^{17} - 8293048100x^{16} + 1782900558x^{15} + 5867612595x^{14} - 1793473521x^{13} - 2855621679x^{12} + 1129637788x^{11} + 893384672x^{10} - 439985654x^{9} - 160236344x^{8} + 100266482x^{7} + 12852552x^{6} - 12313978x^{5} + 51930x^{4} + 703478x^{3} - 55070x^{2} - 12475x + 1385\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 10]$ | $\phantom{-}0$ |
2 | $[2, 2, w - 11]$ | $\phantom{-}e$ |
5 | $[5, 5, -116w - 1171]$ | $...$ |
5 | $[5, 5, 116w - 1287]$ | $...$ |
7 | $[7, 7, -1002w - 10115]$ | $...$ |
7 | $[7, 7, 1002w - 11117]$ | $...$ |
9 | $[9, 3, 3]$ | $...$ |
11 | $[11, 11, 10w - 111]$ | $...$ |
11 | $[11, 11, -10w - 101]$ | $...$ |
23 | $[23, 23, -32w + 355]$ | $...$ |
23 | $[23, 23, 32w + 323]$ | $...$ |
41 | $[41, 41, -8w - 81]$ | $...$ |
41 | $[41, 41, -8w + 89]$ | $...$ |
53 | $[53, 53, 4w - 45]$ | $...$ |
53 | $[53, 53, 4w + 41]$ | $...$ |
59 | $[59, 59, -3892w + 43181]$ | $...$ |
59 | $[59, 59, 3892w + 39289]$ | $...$ |
61 | $[61, 61, 770w - 8543]$ | $...$ |
61 | $[61, 61, -770w - 7773]$ | $...$ |
67 | $[67, 67, 158w + 1595]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w + 10]$ | $1$ |