Properties

Label 3.3.1300.1-19.1-a
Base field 3.3.1300.1
Weight $[2, 2, 2]$
Level norm $19$
Level $[19, 19, -w + 1]$
Dimension $1$
CM no
Base change no

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Base field 3.3.1300.1

Generator \(w\), with minimal polynomial \(x^{3} - 10x - 10\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[19, 19, -w + 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $44$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-2$
5 $[5, 5, -w^{2} + 2w + 5]$ $\phantom{-}1$
7 $[7, 7, w + 3]$ $-2$
11 $[11, 11, -2w^{2} + 5w + 9]$ $\phantom{-}2$
13 $[13, 13, -w^{2} + w + 7]$ $-1$
13 $[13, 13, w - 3]$ $-1$
17 $[17, 17, -w^{2} + 2w + 7]$ $\phantom{-}3$
17 $[17, 17, -2w^{2} + 5w + 7]$ $-2$
17 $[17, 17, -w^{2} + 3w + 3]$ $-7$
19 $[19, 19, -w + 1]$ $-1$
27 $[27, 3, -3]$ $\phantom{-}8$
31 $[31, 31, w^{2} - 2w - 9]$ $\phantom{-}2$
37 $[37, 37, w^{2} - 7]$ $\phantom{-}3$
41 $[41, 41, w^{2} - w - 11]$ $-3$
47 $[47, 47, w^{2} - 3]$ $\phantom{-}8$
49 $[49, 7, w^{2} - 3w - 1]$ $\phantom{-}5$
59 $[59, 59, w^{2} - 4w + 1]$ $-10$
67 $[67, 67, w^{2} - 3w - 7]$ $-12$
71 $[71, 71, 4w + 9]$ $-8$
73 $[73, 73, -4w^{2} + 8w + 23]$ $-1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, -w + 1]$ $1$