Properties

Label 2.2.13.1-1764.1-b
Base field \(\Q(\sqrt{13}) \)
Weight $[2, 2]$
Level norm $1764$
Level $[1764, 42, 42]$
Dimension $1$
CM no
Base change yes

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Base field \(\Q(\sqrt{13}) \)

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

Form

Weight: $[2, 2]$
Level: $[1764, 42, 42]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $47$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w]$ $-1$
3 $[3, 3, -w + 1]$ $-1$
4 $[4, 2, 2]$ $\phantom{-}1$
13 $[13, 13, -2w + 1]$ $\phantom{-}6$
17 $[17, 17, w + 4]$ $\phantom{-}2$
17 $[17, 17, -w + 5]$ $\phantom{-}2$
23 $[23, 23, 3w + 1]$ $\phantom{-}8$
23 $[23, 23, -3w + 4]$ $\phantom{-}8$
25 $[25, 5, 5]$ $-6$
29 $[29, 29, 3w - 2]$ $-2$
29 $[29, 29, -3w + 1]$ $-2$
43 $[43, 43, -4w - 1]$ $-4$
43 $[43, 43, 4w - 5]$ $-4$
49 $[49, 7, -7]$ $\phantom{-}1$
53 $[53, 53, -w - 7]$ $\phantom{-}6$
53 $[53, 53, w - 8]$ $\phantom{-}6$
61 $[61, 61, -3w - 8]$ $\phantom{-}6$
61 $[61, 61, 3w - 11]$ $\phantom{-}6$
79 $[79, 79, 5w - 4]$ $\phantom{-}0$
79 $[79, 79, 5w - 1]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w]$ $1$
$3$ $[3, 3, -w + 1]$ $1$
$4$ $[4, 2, 2]$ $-1$
$49$ $[49, 7, -7]$ $-1$