Properties

Base field \(\Q(\sqrt{114}) \)
Weight [2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 2.2.456.1-1.1-d
Dimension 6
CM yes
Base change yes

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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 $[1, 1, 1]$
Label 2.2.456.1-1.1-d
Dimension 6
Is CM yes
Is base change yes
Parent newspace dimension 62

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 18x^{4} \) \(\mathstrut +\mathstrut 81x^{2} \) \(\mathstrut -\mathstrut 76\)

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Norm Prime Eigenvalue
2 $[2, 2, -3w - 32]$ $\phantom{-}0$
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $\phantom{-}0$
5 $[5, 5, w + 3]$ $\phantom{-}0$
7 $[7, 7, -w + 11]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{11}{4}e^{2} + 3$
7 $[7, 7, w + 11]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{11}{4}e^{2} + 3$
11 $[11, 11, w + 2]$ $\phantom{-}0$
11 $[11, 11, w + 9]$ $\phantom{-}0$
13 $[13, 13, w + 6]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{15}{4}e^{3} + 10e$
13 $[13, 13, w + 7]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{15}{4}e^{3} + 10e$
19 $[19, 19, w]$ $-e^{3} + 9e$
37 $[37, 37, w + 15]$ $-e^{3} + 9e$
37 $[37, 37, w + 22]$ $-e^{3} + 9e$
41 $[41, 41, 37w + 395]$ $\phantom{-}0$
41 $[41, 41, 5w + 53]$ $\phantom{-}0$
67 $[67, 67, w + 28]$ $-\frac{1}{2}e^{5} + \frac{15}{2}e^{3} - 23e$
67 $[67, 67, w + 39]$ $-\frac{1}{2}e^{5} + \frac{15}{2}e^{3} - 23e$
71 $[71, 71, 40w + 427]$ $\phantom{-}0$
71 $[71, 71, 8w + 85]$ $\phantom{-}0$
73 $[73, 73, -2w + 23]$ $\phantom{-}e^{4} - 14e^{2} + 30$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).