Properties

Base field \(\Q(\sqrt{3}) \)
Weight [2, 2]
Level norm 3721
Level $[3721, 61, 61]$
Label 2.2.12.1-3721.1-b
Dimension 1
CM no
Base change yes

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{3}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 3\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[3721, 61, 61]$
Label 2.2.12.1-3721.1-b
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 2

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $-1$
3 $[3, 3, w]$ $-2$
11 $[11, 11, -2w + 1]$ $-5$
11 $[11, 11, 2w + 1]$ $-5$
13 $[13, 13, w + 4]$ $\phantom{-}1$
13 $[13, 13, -w + 4]$ $\phantom{-}1$
23 $[23, 23, -3w + 2]$ $-9$
23 $[23, 23, 3w + 2]$ $-9$
25 $[25, 5, 5]$ $-1$
37 $[37, 37, 2w - 7]$ $\phantom{-}8$
37 $[37, 37, -2w - 7]$ $\phantom{-}8$
47 $[47, 47, -4w - 1]$ $\phantom{-}4$
47 $[47, 47, 4w - 1]$ $\phantom{-}4$
49 $[49, 7, -7]$ $-13$
59 $[59, 59, 5w - 4]$ $\phantom{-}9$
59 $[59, 59, -5w - 4]$ $\phantom{-}9$
61 $[61, 61, -w - 8]$ $-1$
61 $[61, 61, w - 8]$ $-1$
71 $[71, 71, 5w - 2]$ $-8$
71 $[71, 71, -5w - 2]$ $-8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
61 $[61, 61, -w - 8]$ $1$
61 $[61, 61, w - 8]$ $1$