Properties

Base field \(\Q(\sqrt{114}) \)
Weight [2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 2.2.456.1-1.1-f
Dimension 32
CM no
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-f
Dimension 32
Is CM no
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:
\(x^{32} \) \(\mathstrut -\mathstrut 166x^{30} \) \(\mathstrut +\mathstrut 11993x^{28} \) \(\mathstrut -\mathstrut 496380x^{26} \) \(\mathstrut +\mathstrut 13049272x^{24} \) \(\mathstrut -\mathstrut 228590392x^{22} \) \(\mathstrut +\mathstrut 2726867576x^{20} \) \(\mathstrut -\mathstrut 22281994976x^{18} \) \(\mathstrut +\mathstrut 123974635808x^{16} \) \(\mathstrut -\mathstrut 461698065344x^{14} \) \(\mathstrut +\mathstrut 1116269298192x^{12} \) \(\mathstrut -\mathstrut 1671951895104x^{10} \) \(\mathstrut +\mathstrut 1465593782016x^{8} \) \(\mathstrut -\mathstrut 733652793344x^{6} \) \(\mathstrut +\mathstrut 203176308736x^{4} \) \(\mathstrut -\mathstrut 28748431360x^{2} \) \(\mathstrut +\mathstrut 1615396864\)

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Norm Prime Eigenvalue
2 $[2, 2, -3w - 32]$ $...$
3 $[3, 3, w]$ $...$
5 $[5, 5, w + 2]$ $...$
5 $[5, 5, w + 3]$ $...$
7 $[7, 7, -w + 11]$ $...$
7 $[7, 7, w + 11]$ $...$
11 $[11, 11, w + 2]$ $...$
11 $[11, 11, w + 9]$ $...$
13 $[13, 13, w + 6]$ $...$
13 $[13, 13, w + 7]$ $...$
19 $[19, 19, w]$ $...$
37 $[37, 37, w + 15]$ $...$
37 $[37, 37, w + 22]$ $...$
41 $[41, 41, 37w + 395]$ $...$
41 $[41, 41, 5w + 53]$ $...$
67 $[67, 67, w + 28]$ $...$
67 $[67, 67, w + 39]$ $...$
71 $[71, 71, 40w + 427]$ $...$
71 $[71, 71, 8w + 85]$ $...$
73 $[73, 73, -2w + 23]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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