Properties

Base field \(\Q(\sqrt{55}) \)
Weight [2, 2]
Level norm 5
Level $[5, 5, -2w + 15]$
Label 2.2.220.1-5.1-n
Dimension 12
CM no
Base change yes

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Base field \(\Q(\sqrt{55}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 55\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[5, 5, -2w + 15]$
Label 2.2.220.1-5.1-n
Dimension 12
Is CM no
Is base change yes
Parent newspace dimension 60

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} \) \(\mathstrut +\mathstrut 50x^{10} \) \(\mathstrut +\mathstrut 737x^{8} \) \(\mathstrut +\mathstrut 4580x^{6} \) \(\mathstrut +\mathstrut 12472x^{4} \) \(\mathstrut +\mathstrut 12272x^{2} \) \(\mathstrut +\mathstrut 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $-\frac{1783}{202352}e^{11} - \frac{10933}{25294}e^{9} - \frac{1235763}{202352}e^{7} - \frac{3599071}{101176}e^{5} - \frac{1112907}{12647}e^{3} - \frac{956224}{12647}e$
3 $[3, 3, w + 1]$ $\phantom{-}\frac{1783}{202352}e^{11} + \frac{10933}{25294}e^{9} + \frac{1235763}{202352}e^{7} + \frac{3599071}{101176}e^{5} + \frac{1112907}{12647}e^{3} + \frac{968871}{12647}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1783}{202352}e^{11} + \frac{10933}{25294}e^{9} + \frac{1235763}{202352}e^{7} + \frac{3599071}{101176}e^{5} + \frac{1112907}{12647}e^{3} + \frac{968871}{12647}e$
5 $[5, 5, -2w + 15]$ $\phantom{-}1$
11 $[11, 11, 3w - 22]$ $\phantom{-}\frac{2769}{404704}e^{10} + \frac{8415}{25294}e^{8} + \frac{1834449}{404704}e^{6} + \frac{4649041}{202352}e^{4} + \frac{3592341}{101176}e^{2} - \frac{219359}{50588}$
13 $[13, 13, w + 4]$ $\phantom{-}\frac{4863}{809408}e^{11} + \frac{30585}{101176}e^{9} + \frac{3639791}{809408}e^{7} + \frac{11277179}{404704}e^{5} + \frac{15105259}{202352}e^{3} + \frac{7481107}{101176}e$
13 $[13, 13, w + 9]$ $\phantom{-}\frac{4863}{809408}e^{11} + \frac{30585}{101176}e^{9} + \frac{3639791}{809408}e^{7} + \frac{11277179}{404704}e^{5} + \frac{15105259}{202352}e^{3} + \frac{7481107}{101176}e$
17 $[17, 17, w + 2]$ $\phantom{-}\frac{11797}{809408}e^{11} + \frac{73415}{101176}e^{9} + \frac{8579701}{809408}e^{7} + \frac{26343033}{404704}e^{5} + \frac{35310685}{202352}e^{3} + \frac{16981893}{101176}e$
17 $[17, 17, w + 15]$ $\phantom{-}\frac{11797}{809408}e^{11} + \frac{73415}{101176}e^{9} + \frac{8579701}{809408}e^{7} + \frac{26343033}{404704}e^{5} + \frac{35310685}{202352}e^{3} + \frac{16981893}{101176}e$
19 $[19, 19, -w - 6]$ $-\frac{1605}{404704}e^{10} - \frac{18839}{101176}e^{8} - \frac{948317}{404704}e^{6} - \frac{2135331}{202352}e^{4} - \frac{1382717}{101176}e^{2} + \frac{83109}{50588}$
19 $[19, 19, w - 6]$ $-\frac{1605}{404704}e^{10} - \frac{18839}{101176}e^{8} - \frac{948317}{404704}e^{6} - \frac{2135331}{202352}e^{4} - \frac{1382717}{101176}e^{2} + \frac{83109}{50588}$
23 $[23, 23, w + 3]$ $\phantom{-}\frac{961}{404704}e^{11} + \frac{10161}{101176}e^{9} + \frac{359657}{404704}e^{7} - \frac{20581}{202352}e^{5} - \frac{2279835}{101176}e^{3} - \frac{2474109}{50588}e$
23 $[23, 23, w + 20]$ $\phantom{-}\frac{961}{404704}e^{11} + \frac{10161}{101176}e^{9} + \frac{359657}{404704}e^{7} - \frac{20581}{202352}e^{5} - \frac{2279835}{101176}e^{3} - \frac{2474109}{50588}e$
47 $[47, 47, w + 14]$ $-\frac{2883}{404704}e^{11} - \frac{30483}{101176}e^{9} - \frac{1078971}{404704}e^{7} + \frac{61743}{202352}e^{5} + \frac{6839505}{101176}e^{3} + \frac{7422327}{50588}e$
47 $[47, 47, w + 33]$ $-\frac{2883}{404704}e^{11} - \frac{30483}{101176}e^{9} - \frac{1078971}{404704}e^{7} + \frac{61743}{202352}e^{5} + \frac{6839505}{101176}e^{3} + \frac{7422327}{50588}e$
49 $[49, 7, -7]$ $\phantom{-}\frac{4807}{202352}e^{10} + \frac{111483}{101176}e^{8} + \frac{2746203}{202352}e^{6} + \frac{3117455}{50588}e^{4} + \frac{4438231}{50588}e^{2} - \frac{140732}{12647}$
67 $[67, 67, w + 16]$ $-\frac{13605}{404704}e^{11} - \frac{170329}{101176}e^{9} - \frac{10054493}{404704}e^{7} - \frac{31012655}{202352}e^{5} - \frac{41182861}{101176}e^{3} - \frac{19236643}{50588}e$
67 $[67, 67, w + 51]$ $-\frac{13605}{404704}e^{11} - \frac{170329}{101176}e^{9} - \frac{10054493}{404704}e^{7} - \frac{31012655}{202352}e^{5} - \frac{41182861}{101176}e^{3} - \frac{19236643}{50588}e$
73 $[73, 73, w + 36]$ $\phantom{-}\frac{3929}{809408}e^{11} + \frac{31951}{101176}e^{9} + \frac{5681193}{809408}e^{7} + \frac{26711677}{404704}e^{5} + \frac{53702077}{202352}e^{3} + \frac{36576533}{101176}e$
73 $[73, 73, w + 37]$ $\phantom{-}\frac{3929}{809408}e^{11} + \frac{31951}{101176}e^{9} + \frac{5681193}{809408}e^{7} + \frac{26711677}{404704}e^{5} + \frac{53702077}{202352}e^{3} + \frac{36576533}{101176}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w + 15]$ $-1$