Properties

Base field \(\Q(\sqrt{42}) \)
Weight [2, 2]
Level norm 21
Level $[21, 21, w]$
Label 2.2.168.1-21.1-b
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{42}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 42\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[21, 21, w]$
Label 2.2.168.1-21.1-b
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 116

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
3 $[3, 3, w]$ $\phantom{-}1$
7 $[7, 7, w - 7]$ $-1$
11 $[11, 11, w + 3]$ $-4$
11 $[11, 11, w + 8]$ $-4$
13 $[13, 13, w + 4]$ $-2$
13 $[13, 13, w + 9]$ $-2$
17 $[17, 17, -w - 5]$ $\phantom{-}6$
17 $[17, 17, -w + 5]$ $\phantom{-}6$
19 $[19, 19, w + 2]$ $\phantom{-}4$
19 $[19, 19, w + 17]$ $\phantom{-}4$
25 $[25, 5, 5]$ $-6$
29 $[29, 29, w + 10]$ $\phantom{-}2$
29 $[29, 29, w + 19]$ $\phantom{-}2$
41 $[41, 41, -w - 1]$ $-2$
41 $[41, 41, w - 1]$ $-2$
47 $[47, 47, -2w + 11]$ $\phantom{-}0$
47 $[47, 47, 4w - 25]$ $\phantom{-}0$
53 $[53, 53, w + 25]$ $-6$
53 $[53, 53, w + 28]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
7 $[7, 7, w - 7]$ $1$