Properties

Label 2.2.429.1-4.1-h
Base field \(\Q(\sqrt{429}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 2, 2]$
Dimension $2$
CM no
Base change yes

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Base field \(\Q(\sqrt{429}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 107\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[4, 2, 2]$
Dimension: $2$
CM: no
Base change: yes
Newspace dimension: $96$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 11]$ $-2$
4 $[4, 2, 2]$ $\phantom{-}1$
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, w + 3]$ $\phantom{-}e$
7 $[7, 7, w + 1]$ $\phantom{-}3e$
7 $[7, 7, w + 5]$ $\phantom{-}3e$
11 $[11, 11, w + 5]$ $-2e$
13 $[13, 13, w + 6]$ $-3e$
17 $[17, 17, w - 10]$ $\phantom{-}0$
17 $[17, 17, w + 9]$ $\phantom{-}0$
19 $[19, 19, w + 3]$ $\phantom{-}0$
19 $[19, 19, w + 15]$ $\phantom{-}0$
29 $[29, 29, -2w + 21]$ $\phantom{-}6$
29 $[29, 29, 5w - 54]$ $\phantom{-}6$
47 $[47, 47, w + 18]$ $\phantom{-}7e$
47 $[47, 47, w + 28]$ $\phantom{-}7e$
59 $[59, 59, w + 27]$ $-8e$
59 $[59, 59, w + 31]$ $-8e$
71 $[71, 71, w + 21]$ $-5e$
71 $[71, 71, w + 49]$ $-5e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, 2]$ $-1$