Properties

Base field \(\Q(\sqrt{205}) \)
Weight [2, 2]
Level norm 45
Level $[45, 15, -3w + 24]$
Label 2.2.205.1-45.1-b
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{205}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[45, 15, -3w + 24]$
Label 2.2.205.1-45.1-b
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 172

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
3 $[3, 3, w + 2]$ $\phantom{-}1$
4 $[4, 2, 2]$ $-3$
5 $[5, 5, -w + 8]$ $\phantom{-}1$
7 $[7, 7, w + 1]$ $\phantom{-}0$
7 $[7, 7, w + 5]$ $\phantom{-}0$
13 $[13, 13, w + 3]$ $\phantom{-}2$
13 $[13, 13, w + 9]$ $\phantom{-}2$
17 $[17, 17, w]$ $-2$
17 $[17, 17, w + 16]$ $-2$
31 $[31, 31, -w - 4]$ $\phantom{-}0$
31 $[31, 31, w - 5]$ $\phantom{-}0$
41 $[41, 41, 3w - 22]$ $\phantom{-}10$
47 $[47, 47, w + 19]$ $-8$
47 $[47, 47, w + 27]$ $-8$
53 $[53, 53, w + 14]$ $\phantom{-}10$
53 $[53, 53, w + 38]$ $\phantom{-}10$
59 $[59, 59, -w - 10]$ $-4$
59 $[59, 59, w - 11]$ $-4$
61 $[61, 61, 2w - 13]$ $-2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
3 $[3, 3, w + 2]$ $-1$
5 $[5, 5, -w + 8]$ $-1$