Properties

Label 3.3.788.1-16.1-f
Base field 3.3.788.1
Weight $[2, 2, 2]$
Level norm $16$
Level $[16, 4, -2w - 2]$
Dimension $2$
CM no
Base change no

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Base field 3.3.788.1

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

Form

Weight: $[2, 2, 2]$
Level: $[16, 4, -2w - 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 1]$ $\phantom{-}0$
3 $[3, 3, w]$ $\phantom{-}0$
5 $[5, 5, -w^{2} + 2w + 4]$ $\phantom{-}e$
9 $[9, 3, w^{2} - w - 7]$ $-e$
11 $[11, 11, -w^{2} + 2w + 2]$ $\phantom{-}2e$
13 $[13, 13, w - 2]$ $-e$
17 $[17, 17, w^{2} - 2w - 8]$ $\phantom{-}6$
25 $[25, 5, -w^{2} + 2]$ $-e$
31 $[31, 31, 3w^{2} - 5w - 19]$ $\phantom{-}8$
53 $[53, 53, 2w^{2} - 3w - 10]$ $\phantom{-}3e$
53 $[53, 53, w^{2} - 3w - 5]$ $\phantom{-}2$
53 $[53, 53, 2w - 1]$ $-e$
59 $[59, 59, 2w^{2} - 4w - 11]$ $\phantom{-}4$
59 $[59, 59, 2w^{2} - 6w - 5]$ $\phantom{-}4$
59 $[59, 59, 2w + 5]$ $-4$
67 $[67, 67, w^{2} - 3w - 7]$ $-4$
71 $[71, 71, 2w^{2} - 2w - 13]$ $\phantom{-}2e$
73 $[73, 73, 2w^{2} - 4w - 7]$ $-e$
79 $[79, 79, -w^{2} + 10]$ $\phantom{-}6e$
89 $[89, 89, 2w^{2} - w - 10]$ $\phantom{-}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

The Atkin-Lehner eigenvalues for this form are not in the database.