Properties

Label 2.2.449.1-8.3-b
Base field \(\Q(\sqrt{449}) \)
Weight $[2, 2]$
Level norm $8$
Level $[8, 8, 443w + 4472]$
Dimension $42$
CM no
Base change no

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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 $[67, 67, 158w + 1595]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w + 10]$ $1$