Properties

Label 2.2.109.1-15.1-a
Base field \(\Q(\sqrt{109}) \)
Weight $[2, 2]$
Level norm $15$
Level $[15, 15, -w - 3]$
Dimension $1$
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: $[15, 15, -w - 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $21$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $-1$
3 $[3, 3, w + 5]$ $-3$
4 $[4, 2, 2]$ $\phantom{-}2$
5 $[5, 5, -3w + 17]$ $-2$
5 $[5, 5, -3w - 14]$ $\phantom{-}1$
7 $[7, 7, w - 5]$ $\phantom{-}3$
7 $[7, 7, w + 4]$ $-2$
29 $[29, 29, -w - 7]$ $-1$
29 $[29, 29, -w + 8]$ $\phantom{-}4$
31 $[31, 31, -5w + 28]$ $\phantom{-}2$
31 $[31, 31, -5w - 23]$ $-4$
43 $[43, 43, 6w + 29]$ $\phantom{-}8$
43 $[43, 43, -6w + 35]$ $-11$
61 $[61, 61, 3w - 19]$ $-12$
61 $[61, 61, -3w - 16]$ $-10$
71 $[71, 71, -7w - 34]$ $\phantom{-}14$
71 $[71, 71, 7w - 41]$ $-15$
73 $[73, 73, 2w - 7]$ $\phantom{-}8$
73 $[73, 73, -2w - 5]$ $\phantom{-}3$
83 $[83, 83, -w - 10]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w + 6]$ $1$
$5$ $[5, 5, -3w - 14]$ $-1$