Properties

Base field \(\Q(\sqrt{5}) \)
Weight [2, 2]
Level norm 3249
Level $[3249, 57, 57]$
Label 2.2.5.1-3249.1-g
Dimension 1
CM no
Base change yes

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{5}) \)

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

Form

Weight [2, 2]
Level $[3249, 57, 57]$
Label 2.2.5.1-3249.1-g
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 41

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}0$
5 $[5, 5, -2w + 1]$ $-3$
9 $[9, 3, 3]$ $\phantom{-}1$
11 $[11, 11, -3w + 2]$ $\phantom{-}1$
11 $[11, 11, -3w + 1]$ $\phantom{-}1$
19 $[19, 19, -4w + 3]$ $-1$
19 $[19, 19, -4w + 1]$ $-1$
29 $[29, 29, w + 5]$ $-2$
29 $[29, 29, -w + 6]$ $-2$
31 $[31, 31, -5w + 2]$ $-6$
31 $[31, 31, -5w + 3]$ $-6$
41 $[41, 41, -6w + 5]$ $\phantom{-}0$
41 $[41, 41, w - 7]$ $\phantom{-}0$
49 $[49, 7, -7]$ $\phantom{-}11$
59 $[59, 59, 2w - 9]$ $-8$
59 $[59, 59, 7w - 5]$ $-8$
61 $[61, 61, 3w - 10]$ $-1$
61 $[61, 61, -3w - 7]$ $-1$
71 $[71, 71, -8w + 7]$ $-12$
71 $[71, 71, w - 9]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, 3]$ $-1$
19 $[19, 19, -4w + 3]$ $1$
19 $[19, 19, -4w + 1]$ $1$