Properties

Base field \(\Q(\sqrt{109}) \)
Weight [2, 2]
Level norm 9
Level $[9, 3, 3]$
Label 2.2.109.1-9.1-a
Dimension 2
CM no
Base change yes

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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 $[9, 3, 3]$
Label 2.2.109.1-9.1-a
Dimension 2
Is CM no
Is base change yes
Parent newspace dimension 13

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut -\mathstrut 2x \) \(\mathstrut -\mathstrut 5\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $1$
3 $[3, 3, w + 5]$ $1$