Properties

Label 3.3.229.1-37.2-c
Base field 3.3.229.1
Weight $[2, 2, 2]$
Level norm $37$
Level $[37, 37, -2w^{2} + 5]$
Dimension $1$
CM no
Base change no

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Base field 3.3.229.1

Generator \(w\), with minimal polynomial \(x^{3} - 4x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[37, 37, -2w^{2} + 5]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}0$
4 $[4, 2, -w^{2} + w + 3]$ $-2$
7 $[7, 7, w^{2} - 2]$ $-2$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}1$
23 $[23, 23, -2w + 1]$ $\phantom{-}0$
27 $[27, 3, 3]$ $\phantom{-}1$
29 $[29, 29, -2w + 3]$ $-3$
31 $[31, 31, -2w^{2} + 2w + 3]$ $-5$
37 $[37, 37, 4w^{2} - 2w - 13]$ $-2$
37 $[37, 37, -2w^{2} + 5]$ $-1$
37 $[37, 37, 2w^{2} - w - 10]$ $\phantom{-}2$
41 $[41, 41, w^{2} - 2w - 4]$ $-9$
47 $[47, 47, w - 4]$ $\phantom{-}6$
49 $[49, 7, 2w^{2} - w - 4]$ $\phantom{-}4$
53 $[53, 53, 2w^{2} - 2w - 7]$ $-3$
53 $[53, 53, 3w^{2} - 2w - 8]$ $\phantom{-}9$
53 $[53, 53, 2w + 5]$ $-3$
59 $[59, 59, 2w^{2} - 2w - 9]$ $-12$
67 $[67, 67, 2w^{2} - 3]$ $-14$
73 $[73, 73, 2w^{2} + w - 8]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37, 37, -2w^{2} + 5]$ $1$