Properties

Label 2.2.481.1-2.1-d
Base field \(\Q(\sqrt{481}) \)
Weight $[2, 2]$
Level norm $2$
Level $[2, 2, w]$
Dimension $18$
CM no
Base change no

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Base field \(\Q(\sqrt{481}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 120\); narrow class number \(2\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[2, 2, w]$
Dimension: $18$
CM: no
Base change: no
Newspace dimension: $60$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{18} + 22x^{16} + 199x^{14} + 962x^{12} + 2695x^{10} + 4414x^{8} + 4014x^{6} + 1740x^{4} + 229x^{2} + 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}4e^{17} + \frac{242}{3}e^{15} + 648e^{13} + 2658e^{11} + 5893e^{9} + 6803e^{7} + \frac{10471}{3}e^{5} + 464e^{3} + \frac{43}{3}e$
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -2w - 21]$ $\phantom{-}\frac{28}{3}e^{16} + \frac{565}{3}e^{14} + \frac{4544}{3}e^{12} + \frac{18682}{3}e^{10} + \frac{41615}{3}e^{8} + 16182e^{6} + \frac{25624}{3}e^{4} + \frac{3901}{3}e^{2} + 59$
3 $[3, 3, 2w - 23]$ $-\frac{20}{3}e^{16} - \frac{403}{3}e^{14} - \frac{3233}{3}e^{12} - \frac{13231}{3}e^{10} - \frac{29210}{3}e^{8} - \frac{33422}{3}e^{6} - \frac{16753}{3}e^{4} - 665e^{2} - 22$
5 $[5, 5, w]$ $\phantom{-}5e^{17} + \frac{307}{3}e^{15} + \frac{2522}{3}e^{13} + \frac{10717}{3}e^{11} + \frac{25211}{3}e^{9} + \frac{32455}{3}e^{7} + \frac{21028}{3}e^{5} + \frac{5567}{3}e^{3} + 120e$
5 $[5, 5, w + 4]$ $\phantom{-}6e^{17} + 122e^{15} + 992e^{13} + 4146e^{11} + 9483e^{9} + 11604e^{7} + 6797e^{5} + 1432e^{3} + 82e$
13 $[13, 13, w + 6]$ $\phantom{-}12e^{17} + 242e^{15} + 1944e^{13} + 7974e^{11} + 17679e^{9} + 20409e^{7} + 10471e^{5} + 1392e^{3} + 44e$
19 $[19, 19, w + 2]$ $-\frac{35}{3}e^{17} - \frac{703}{3}e^{15} - \frac{5615}{3}e^{13} - \frac{22837}{3}e^{11} - \frac{49946}{3}e^{9} - \frac{56231}{3}e^{7} - \frac{27163}{3}e^{5} - 879e^{3} - 8e$
19 $[19, 19, w + 16]$ $-9e^{17} - \frac{544}{3}e^{15} - \frac{4367}{3}e^{13} - \frac{17914}{3}e^{11} - \frac{39797}{3}e^{9} - \frac{46282}{3}e^{7} - \frac{24364}{3}e^{5} - \frac{3722}{3}e^{3} - 53e$
31 $[31, 31, w + 13]$ $-9e^{17} - 183e^{15} - 1488e^{13} - 6219e^{11} - 14225e^{9} - 17412e^{7} - 10217e^{5} - 2168e^{3} - 114e$
31 $[31, 31, w + 17]$ $\phantom{-}4e^{15} + 80e^{13} + 636e^{11} + 2574e^{9} + 5598e^{7} + 6244e^{5} + 2928e^{3} + 216e$
37 $[37, 37, w + 18]$ $-7e^{17} - 139e^{15} - 1090e^{13} - 4296e^{11} - 8852e^{9} - 8693e^{7} - 2519e^{5} + 840e^{3} + 82e$
49 $[49, 7, -7]$ $\phantom{-}57e^{16} + 1148e^{14} + 9208e^{12} + 37707e^{10} + 83458e^{8} + 96214e^{6} + 49394e^{4} + 6707e^{2} + 257$
53 $[53, 53, -234w + 2683]$ $-\frac{16}{3}e^{16} - \frac{319}{3}e^{14} - \frac{2513}{3}e^{12} - \frac{9955}{3}e^{10} - \frac{20636}{3}e^{8} - 6820e^{6} - \frac{6163}{3}e^{4} + \frac{1832}{3}e^{2} + 69$
53 $[53, 53, -234w - 2449]$ $\phantom{-}30e^{16} + 605e^{14} + 4859e^{12} + 19919e^{10} + 44105e^{8} + 50789e^{6} + 25942e^{4} + 3432e^{2} + 123$
59 $[59, 59, w + 1]$ $-5e^{17} - 99e^{15} - 774e^{13} - 3043e^{11} - 6269e^{9} - 6210e^{7} - 1937e^{5} + 468e^{3} + 32e$
59 $[59, 59, w + 57]$ $-\frac{139}{3}e^{17} - 935e^{15} - 7522e^{13} - 30950e^{11} - 69065e^{9} - \frac{242675}{3}e^{7} - 43149e^{5} - \frac{20576}{3}e^{3} - 321e$
89 $[89, 89, w + 41]$ $\phantom{-}\frac{19}{3}e^{17} + \frac{377}{3}e^{15} + \frac{2953}{3}e^{13} + \frac{11621}{3}e^{11} + \frac{23908}{3}e^{9} + \frac{23485}{3}e^{7} + \frac{6917}{3}e^{5} - 743e^{3} - 104e$
89 $[89, 89, w + 47]$ $-7e^{17} - 146e^{15} - 1232e^{13} - 5442e^{11} - 13557e^{9} - 19044e^{7} - 14139e^{5} - 4623e^{3} - 347e$
97 $[97, 97, w + 26]$ $\phantom{-}\frac{67}{3}e^{17} + \frac{1343}{3}e^{15} + \frac{10696}{3}e^{13} + \frac{43313}{3}e^{11} + \frac{94021}{3}e^{9} + \frac{104200}{3}e^{7} + \frac{48035}{3}e^{5} + 1003e^{3} - 57e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-4e^{17} - \frac{242}{3}e^{15} - 648e^{13} - 2658e^{11} - 5893e^{9} - 6803e^{7} - \frac{10471}{3}e^{5} - 464e^{3} - \frac{43}{3}e$