Properties

Label 2.2.184.1-12.1-d
Base field \(\Q(\sqrt{46}) \)
Weight $[2, 2]$
Level norm $12$
Level $[12, 6, -2w - 14]$
Dimension $6$
CM no
Base change no

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Base field \(\Q(\sqrt{46}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 46\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[12, 6, -2w - 14]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{6} - 20x^{4} + 100x^{2} - 98\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, 23w - 156]$ $\phantom{-}0$
3 $[3, 3, -w - 7]$ $\phantom{-}1$
3 $[3, 3, w - 7]$ $-\frac{1}{7}e^{4} + \frac{17}{7}e^{2} - 6$
5 $[5, 5, -9w + 61]$ $\phantom{-}e$
5 $[5, 5, -9w - 61]$ $-\frac{1}{7}e^{3} + \frac{10}{7}e$
7 $[7, 7, 4w - 27]$ $\phantom{-}e$
7 $[7, 7, 4w + 27]$ $\phantom{-}\frac{1}{7}e^{5} - \frac{16}{7}e^{3} + \frac{46}{7}e$
23 $[23, 23, 78w - 529]$ $\phantom{-}\frac{1}{7}e^{5} - \frac{16}{7}e^{3} + \frac{53}{7}e$
37 $[37, 37, -w - 3]$ $-\frac{1}{7}e^{5} + \frac{15}{7}e^{3} - \frac{43}{7}e$
37 $[37, 37, w - 3]$ $\phantom{-}\frac{1}{7}e^{5} - \frac{18}{7}e^{3} + \frac{59}{7}e$
41 $[41, 41, -2w + 15]$ $\phantom{-}\frac{3}{7}e^{4} - \frac{44}{7}e^{2} + 12$
41 $[41, 41, 2w + 15]$ $-\frac{2}{7}e^{4} + \frac{27}{7}e^{2} - 4$
53 $[53, 53, -3w - 19]$ $\phantom{-}\frac{1}{7}e^{5} - \frac{16}{7}e^{3} + \frac{39}{7}e$
53 $[53, 53, 3w - 19]$ $\phantom{-}\frac{1}{7}e^{5} - 3e^{3} + \frac{82}{7}e$
59 $[59, 59, 11w - 75]$ $-\frac{3}{7}e^{4} + \frac{44}{7}e^{2} - 20$
59 $[59, 59, -11w - 75]$ $-\frac{1}{7}e^{4} + \frac{24}{7}e^{2} - 14$
61 $[61, 61, -5w + 33]$ $-\frac{1}{7}e^{5} + \frac{13}{7}e^{3} - \frac{30}{7}e$
61 $[61, 61, 5w + 33]$ $-\frac{1}{7}e^{3} + \frac{10}{7}e$
73 $[73, 73, -24w - 163]$ $-\frac{3}{7}e^{4} + \frac{44}{7}e^{2} - 14$
73 $[73, 73, -24w + 163]$ $\phantom{-}\frac{3}{7}e^{4} - \frac{44}{7}e^{2} + 22$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, 23w - 156]$ $-1$
$3$ $[3, 3, -w - 7]$ $-1$