Properties

Label 3.3.1901.1-13.2-b
Base field 3.3.1901.1
Weight $[2, 2, 2]$
Level norm $13$
Level $[13, 13, -w + 3]$
Dimension $1$
CM no
Base change no

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Base field 3.3.1901.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 4\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[13, 13, -w + 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $53$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w + 2]$ $\phantom{-}2$
3 $[3, 3, w + 1]$ $\phantom{-}0$
4 $[4, 2, -w^{2} + 3w + 3]$ $\phantom{-}3$
9 $[9, 3, -w^{2} + 2w + 7]$ $-1$
13 $[13, 13, w + 3]$ $\phantom{-}4$
13 $[13, 13, -w + 3]$ $-1$
13 $[13, 13, -w + 1]$ $-4$
17 $[17, 17, -w^{2} - 2w + 1]$ $\phantom{-}2$
23 $[23, 23, w^{2} - 2w - 5]$ $-8$
31 $[31, 31, 2w + 3]$ $-8$
31 $[31, 31, -2w^{2} + 3w + 15]$ $-10$
31 $[31, 31, 3w + 7]$ $-6$
37 $[37, 37, 3w^{2} - 4w - 27]$ $\phantom{-}1$
41 $[41, 41, -2w^{2} + 7w + 1]$ $\phantom{-}0$
59 $[59, 59, w^{2} - 3]$ $-4$
61 $[61, 61, 4w^{2} - 12w - 11]$ $-4$
71 $[71, 71, w^{2} - 2w - 11]$ $-13$
97 $[97, 97, 3w + 5]$ $\phantom{-}17$
101 $[101, 101, 2w^{2} - 6w - 7]$ $\phantom{-}15$
103 $[103, 103, 2w^{2} - 3w - 19]$ $\phantom{-}11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w + 3]$ $1$