Properties

Label 2.2.184.1-10.1-h
Base field \(\Q(\sqrt{46}) \)
Weight $[2, 2]$
Level norm $10$
Level $[10, 10, w - 6]$
Dimension $3$
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: $[10, 10, w - 6]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 9x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, 23w - 156]$ $-1$
3 $[3, 3, -w - 7]$ $\phantom{-}e$
3 $[3, 3, w - 7]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e - \frac{8}{3}$
5 $[5, 5, -9w + 61]$ $-\frac{1}{3}e^{2} + \frac{2}{3}e + \frac{8}{3}$
5 $[5, 5, -9w - 61]$ $-1$
7 $[7, 7, 4w - 27]$ $\phantom{-}e + 1$
7 $[7, 7, 4w + 27]$ $-\frac{1}{3}e^{2} + \frac{2}{3}e + \frac{5}{3}$
23 $[23, 23, 78w - 529]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e + \frac{7}{3}$
37 $[37, 37, -w - 3]$ $\phantom{-}\frac{4}{3}e^{2} - \frac{2}{3}e - \frac{23}{3}$
37 $[37, 37, w - 3]$ $-e + 6$
41 $[41, 41, -2w + 15]$ $\phantom{-}\frac{2}{3}e^{2} + \frac{2}{3}e - \frac{13}{3}$
41 $[41, 41, 2w + 15]$ $-\frac{2}{3}e^{2} - \frac{5}{3}e + \frac{16}{3}$
53 $[53, 53, -3w - 19]$ $\phantom{-}e^{2} - 2e - 11$
53 $[53, 53, 3w - 19]$ $-\frac{2}{3}e^{2} + \frac{4}{3}e + \frac{43}{3}$
59 $[59, 59, 11w - 75]$ $-e^{2} + 1$
59 $[59, 59, -11w - 75]$ $-\frac{5}{3}e^{2} - \frac{2}{3}e + \frac{25}{3}$
61 $[61, 61, -5w + 33]$ $-\frac{2}{3}e^{2} + \frac{1}{3}e + \frac{7}{3}$
61 $[61, 61, 5w + 33]$ $-\frac{1}{3}e^{2} - \frac{4}{3}e + \frac{20}{3}$
73 $[73, 73, -24w - 163]$ $-\frac{2}{3}e^{2} - \frac{2}{3}e - \frac{8}{3}$
73 $[73, 73, -24w + 163]$ $-e^{2} + e + 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, 23w - 156]$ $1$
$5$ $[5, 5, -9w - 61]$ $1$