Properties

Base field \(\Q(\sqrt{55}) \)
Weight [2, 2]
Level norm 5
Level $[5, 5, -2w + 15]$
Label 2.2.220.1-5.1-m
Dimension 8
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-m
Dimension 8
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:
\(x^{8} \) \(\mathstrut +\mathstrut 26x^{6} \) \(\mathstrut +\mathstrut 157x^{4} \) \(\mathstrut +\mathstrut 264x^{2} \) \(\mathstrut +\mathstrut 36\)

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Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}\frac{1}{396}e^{7} + \frac{19}{198}e^{5} + \frac{415}{396}e^{3} + \frac{181}{66}e$
3 $[3, 3, w + 1]$ $-\frac{1}{396}e^{7} - \frac{19}{198}e^{5} - \frac{415}{396}e^{3} - \frac{115}{66}e$
3 $[3, 3, w + 2]$ $-\frac{1}{396}e^{7} - \frac{19}{198}e^{5} - \frac{415}{396}e^{3} - \frac{115}{66}e$
5 $[5, 5, -2w + 15]$ $-1$
11 $[11, 11, 3w - 22]$ $-\frac{2}{33}e^{6} - \frac{43}{33}e^{4} - \frac{137}{33}e^{2} - \frac{20}{11}$
13 $[13, 13, w + 4]$ $-\frac{1}{198}e^{7} - \frac{19}{99}e^{5} - \frac{415}{198}e^{3} - \frac{181}{33}e$
13 $[13, 13, w + 9]$ $-\frac{1}{198}e^{7} - \frac{19}{99}e^{5} - \frac{415}{198}e^{3} - \frac{181}{33}e$
17 $[17, 17, w + 2]$ $-\frac{17}{396}e^{7} - \frac{112}{99}e^{5} - \frac{2897}{396}e^{3} - \frac{1031}{66}e$
17 $[17, 17, w + 15]$ $-\frac{17}{396}e^{7} - \frac{112}{99}e^{5} - \frac{2897}{396}e^{3} - \frac{1031}{66}e$
19 $[19, 19, -w - 6]$ $\phantom{-}\frac{3}{22}e^{6} + \frac{35}{11}e^{4} + \frac{299}{22}e^{2} + \frac{100}{11}$
19 $[19, 19, w - 6]$ $\phantom{-}\frac{3}{22}e^{6} + \frac{35}{11}e^{4} + \frac{299}{22}e^{2} + \frac{100}{11}$
23 $[23, 23, w + 3]$ $\phantom{-}\frac{23}{198}e^{7} + \frac{577}{198}e^{5} + \frac{1555}{99}e^{3} + \frac{632}{33}e$
23 $[23, 23, w + 20]$ $\phantom{-}\frac{23}{198}e^{7} + \frac{577}{198}e^{5} + \frac{1555}{99}e^{3} + \frac{632}{33}e$
47 $[47, 47, w + 14]$ $\phantom{-}\frac{23}{198}e^{7} + \frac{577}{198}e^{5} + \frac{1555}{99}e^{3} + \frac{632}{33}e$
47 $[47, 47, w + 33]$ $\phantom{-}\frac{23}{198}e^{7} + \frac{577}{198}e^{5} + \frac{1555}{99}e^{3} + \frac{632}{33}e$
49 $[49, 7, -7]$ $\phantom{-}\frac{2}{33}e^{6} + \frac{43}{33}e^{4} + \frac{104}{33}e^{2} - \frac{145}{11}$
67 $[67, 67, w + 16]$ $-\frac{4}{33}e^{7} - \frac{205}{66}e^{5} - \frac{1175}{66}e^{3} - \frac{249}{11}e$
67 $[67, 67, w + 51]$ $-\frac{4}{33}e^{7} - \frac{205}{66}e^{5} - \frac{1175}{66}e^{3} - \frac{249}{11}e$
73 $[73, 73, w + 36]$ $\phantom{-}\frac{1}{198}e^{7} + \frac{19}{99}e^{5} + \frac{415}{198}e^{3} + \frac{181}{33}e$
73 $[73, 73, w + 37]$ $\phantom{-}\frac{1}{198}e^{7} + \frac{19}{99}e^{5} + \frac{415}{198}e^{3} + \frac{181}{33}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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