Properties

Label 2.2.53.1-37.1-a
Base field \(\Q(\sqrt{53}) \)
Weight $[2, 2]$
Level norm $37$
Level $[37, 37, 2w - 5]$
Dimension $1$
CM no
Base change no

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Base field \(\Q(\sqrt{53}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 13\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[37, 37, 2w - 5]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}1$
7 $[7, 7, w + 2]$ $-1$
7 $[7, 7, w - 3]$ $\phantom{-}3$
9 $[9, 3, 3]$ $-1$
11 $[11, 11, w + 1]$ $\phantom{-}5$
11 $[11, 11, w - 2]$ $-4$
13 $[13, 13, w]$ $\phantom{-}4$
13 $[13, 13, w - 1]$ $-2$
17 $[17, 17, -w - 5]$ $\phantom{-}3$
17 $[17, 17, w - 6]$ $\phantom{-}8$
25 $[25, 5, -5]$ $\phantom{-}2$
29 $[29, 29, -w - 6]$ $\phantom{-}10$
29 $[29, 29, w - 7]$ $-6$
37 $[37, 37, 2w - 5]$ $-1$
37 $[37, 37, -2w - 3]$ $-5$
43 $[43, 43, -w - 7]$ $-1$
43 $[43, 43, w - 8]$ $-12$
47 $[47, 47, 3w + 7]$ $-6$
47 $[47, 47, 3w - 10]$ $\phantom{-}8$
53 $[53, 53, 2w - 1]$ $\phantom{-}12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37, 37, 2w - 5]$ $1$