Properties

Base field \(\Q(\sqrt{114}) \)
Weight [2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 2.2.456.1-1.1-c
Dimension 4
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-c
Dimension 4
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:
\(x^{4} \) \(\mathstrut +\mathstrut 16x^{2} \) \(\mathstrut +\mathstrut 144\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -3w - 32]$ $-\frac{1}{24}e^{3} - \frac{1}{6}e$
3 $[3, 3, w]$ $-\frac{1}{24}e^{3} - \frac{7}{6}e$
5 $[5, 5, w + 2]$ $\phantom{-}\frac{1}{4}e^{2} + 2$
5 $[5, 5, w + 3]$ $\phantom{-}\frac{1}{4}e^{2} + 2$
7 $[7, 7, -w + 11]$ $\phantom{-}1$
7 $[7, 7, w + 11]$ $\phantom{-}1$
11 $[11, 11, w + 2]$ $-\frac{1}{4}e^{2} - 2$
11 $[11, 11, w + 9]$ $-\frac{1}{4}e^{2} - 2$
13 $[13, 13, w + 6]$ $\phantom{-}\frac{1}{24}e^{3} + \frac{7}{6}e$
13 $[13, 13, w + 7]$ $\phantom{-}\frac{1}{24}e^{3} + \frac{7}{6}e$
19 $[19, 19, w]$ $-\frac{1}{12}e^{3} - \frac{7}{3}e$
37 $[37, 37, w + 15]$ $\phantom{-}\frac{1}{8}e^{3} + \frac{7}{2}e$
37 $[37, 37, w + 22]$ $\phantom{-}\frac{1}{8}e^{3} + \frac{7}{2}e$
41 $[41, 41, 37w + 395]$ $-\frac{7}{24}e^{3} - \frac{7}{6}e$
41 $[41, 41, 5w + 53]$ $-\frac{7}{24}e^{3} - \frac{7}{6}e$
67 $[67, 67, w + 28]$ $\phantom{-}\frac{1}{12}e^{3} + \frac{7}{3}e$
67 $[67, 67, w + 39]$ $\phantom{-}\frac{1}{12}e^{3} + \frac{7}{3}e$
71 $[71, 71, 40w + 427]$ $-\frac{1}{8}e^{3} - \frac{1}{2}e$
71 $[71, 71, 8w + 85]$ $-\frac{1}{8}e^{3} - \frac{1}{2}e$
73 $[73, 73, -2w + 23]$ $-3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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