Properties

Label 3.3.697.1-37.1-a
Base field 3.3.697.1
Weight $[2, 2, 2]$
Level norm $37$
Level $[37, 37, w^{2} - 2w - 6]$
Dimension $1$
CM no
Base change no

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Base field 3.3.697.1

Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[37, 37, w^{2} - 2w - 6]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}2$
8 $[8, 2, 2]$ $-1$
11 $[11, 11, -w^{2} + 2w + 4]$ $-4$
11 $[11, 11, -w + 2]$ $\phantom{-}0$
11 $[11, 11, w - 1]$ $-2$
13 $[13, 13, -w^{2} + w + 4]$ $-4$
17 $[17, 17, -w^{2} + w + 8]$ $\phantom{-}2$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}0$
19 $[19, 19, -w^{2} + 6]$ $-2$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}6$
25 $[25, 5, w^{2} - 7]$ $\phantom{-}2$
27 $[27, 3, -3]$ $\phantom{-}0$
31 $[31, 31, w^{2} - 2w - 8]$ $-8$
37 $[37, 37, w^{2} - 2w - 6]$ $-1$
41 $[41, 41, -w - 4]$ $\phantom{-}2$
41 $[41, 41, w^{2} - 2w - 7]$ $\phantom{-}6$
47 $[47, 47, 2w^{2} - 3w - 7]$ $-6$
53 $[53, 53, -w^{2} + w + 9]$ $-6$
61 $[61, 61, 3w^{2} - 2w - 17]$ $\phantom{-}8$
67 $[67, 67, 2w - 1]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37, 37, w^{2} - 2w - 6]$ $1$