Properties

Label 2.2.109.1-12.1-f
Base field \(\Q(\sqrt{109}) \)
Weight $[2, 2]$
Level norm $12$
Level $[12, 6, -2w + 12]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\sqrt{109}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 27\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[12, 6, -2w + 12]$
Dimension: $2$
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:

\(x^{2} + 3x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $\phantom{-}1$
3 $[3, 3, w + 5]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-1$
5 $[5, 5, -3w + 17]$ $\phantom{-}2$
5 $[5, 5, -3w - 14]$ $-e - 3$
7 $[7, 7, w - 5]$ $-e$
7 $[7, 7, w + 4]$ $\phantom{-}e + 1$
29 $[29, 29, -w - 7]$ $\phantom{-}2e - 2$
29 $[29, 29, -w + 8]$ $-3e - 9$
31 $[31, 31, -5w + 28]$ $\phantom{-}2e + 4$
31 $[31, 31, -5w - 23]$ $-6$
43 $[43, 43, 6w + 29]$ $\phantom{-}e - 4$
43 $[43, 43, -6w + 35]$ $\phantom{-}e - 4$
61 $[61, 61, 3w - 19]$ $-8$
61 $[61, 61, -3w - 16]$ $\phantom{-}4e + 12$
71 $[71, 71, -7w - 34]$ $\phantom{-}3e - 4$
71 $[71, 71, 7w - 41]$ $\phantom{-}2e$
73 $[73, 73, 2w - 7]$ $\phantom{-}8$
73 $[73, 73, -2w - 5]$ $-2e - 2$
83 $[83, 83, -w - 10]$ $\phantom{-}6e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w + 6]$ $-1$
$4$ $[4, 2, 2]$ $1$