Properties

Base field \(\Q(\sqrt{114}) \)
Weight [2, 2]
Level norm 3
Level $[3, 3, w]$
Label 2.2.456.1-3.1-e
Dimension 8
CM no
Base change no

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Base field \(\Q(\sqrt{114}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 114\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[3, 3, w]$
Label 2.2.456.1-3.1-e
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 72

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut -\mathstrut 19x^{6} \) \(\mathstrut +\mathstrut 87x^{4} \) \(\mathstrut -\mathstrut 116x^{2} \) \(\mathstrut +\mathstrut 16\)

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Norm Prime Eigenvalue
2 $[2, 2, -3w - 32]$ $\phantom{-}\frac{1}{76}e^{7} - \frac{9}{76}e^{5} - \frac{79}{76}e^{3} + \frac{155}{38}e$
3 $[3, 3, w]$ $\phantom{-}1$
5 $[5, 5, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 3]$ $-\frac{1}{76}e^{7} + \frac{9}{76}e^{5} + \frac{79}{76}e^{3} - \frac{193}{38}e$
7 $[7, 7, -w + 11]$ $-\frac{3}{76}e^{6} + \frac{65}{76}e^{4} - \frac{333}{76}e^{2} + \frac{62}{19}$
7 $[7, 7, w + 11]$ $\phantom{-}\frac{2}{19}e^{6} - \frac{37}{19}e^{4} + \frac{146}{19}e^{2} - \frac{83}{19}$
11 $[11, 11, w + 2]$ $\phantom{-}\frac{5}{76}e^{7} - \frac{83}{76}e^{5} + \frac{251}{76}e^{3} - \frac{40}{19}e$
11 $[11, 11, w + 9]$ $-\frac{21}{152}e^{7} + \frac{379}{152}e^{5} - \frac{1495}{152}e^{3} + \frac{179}{19}e$
13 $[13, 13, w + 6]$ $\phantom{-}\frac{1}{38}e^{6} - \frac{9}{38}e^{4} - \frac{79}{38}e^{2} + \frac{117}{19}$
13 $[13, 13, w + 7]$ $-\frac{3}{19}e^{6} + \frac{46}{19}e^{4} - \frac{86}{19}e^{2} - \frac{56}{19}$
19 $[19, 19, w]$ $-\frac{5}{38}e^{6} + \frac{83}{38}e^{4} - \frac{251}{38}e^{2} + \frac{23}{19}$
37 $[37, 37, w + 15]$ $-\frac{17}{76}e^{6} + \frac{267}{76}e^{4} - \frac{595}{76}e^{2} - \frac{111}{19}$
37 $[37, 37, w + 22]$ $-\frac{3}{76}e^{6} + \frac{65}{76}e^{4} - \frac{409}{76}e^{2} + \frac{62}{19}$
41 $[41, 41, 37w + 395]$ $-\frac{15}{152}e^{7} + \frac{249}{152}e^{5} - \frac{829}{152}e^{3} + \frac{174}{19}e$
41 $[41, 41, 5w + 53]$ $\phantom{-}\frac{37}{76}e^{7} - \frac{675}{76}e^{5} + \frac{2739}{76}e^{3} - \frac{714}{19}e$
67 $[67, 67, w + 28]$ $\phantom{-}\frac{4}{19}e^{6} - \frac{74}{19}e^{4} + \frac{311}{19}e^{2} - \frac{318}{19}$
67 $[67, 67, w + 39]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{15}{4}e^{4} + \frac{27}{4}e^{2}$
71 $[71, 71, 40w + 427]$ $\phantom{-}\frac{5}{38}e^{7} - \frac{32}{19}e^{5} - \frac{36}{19}e^{3} + \frac{809}{38}e$
71 $[71, 71, 8w + 85]$ $-\frac{17}{152}e^{7} + \frac{343}{152}e^{5} - \frac{1811}{152}e^{3} + \frac{277}{19}e$
73 $[73, 73, -2w + 23]$ $-\frac{8}{19}e^{6} + \frac{129}{19}e^{4} - \frac{337}{19}e^{2} + \frac{47}{19}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$