Properties

Label 3.3.1229.1-16.1-a
Base field 3.3.1229.1
Weight $[2, 2, 2]$
Level norm $16$
Level $[16, 4, 2w^{2} + 4w - 4]$
Dimension $3$
CM no
Base change no

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Base field 3.3.1229.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 6\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[16, 4, 2w^{2} + 4w - 4]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + 2x^{2} - 5x - 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{2} + 2w - 2]$ $\phantom{-}0$
3 $[3, 3, -w + 3]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + w + 5]$ $-1$
9 $[9, 3, w^{2} + 2w - 1]$ $\phantom{-}e^{2} - e - 4$
11 $[11, 11, w + 1]$ $\phantom{-}e^{2} - 1$
13 $[13, 13, -2w^{2} - 3w + 5]$ $-2e^{2} + e + 9$
17 $[17, 17, -2w + 5]$ $-e^{2} + e + 4$
19 $[19, 19, -w^{2} + 5]$ $\phantom{-}e^{2} - 1$
23 $[23, 23, -w^{2} + 2w + 1]$ $\phantom{-}3e^{2} + e - 10$
29 $[29, 29, 3w^{2} + 6w - 5]$ $-e^{2} + e + 9$
37 $[37, 37, 4w^{2} - 2w - 25]$ $\phantom{-}e^{2} + 2e + 2$
67 $[67, 67, 2w^{2} + 2w - 7]$ $\phantom{-}0$
67 $[67, 67, -2w^{2} - 5w + 1]$ $-6e^{2} - 2e + 27$
67 $[67, 67, 2w^{2} + 3w - 7]$ $-4e^{2} + e + 23$
71 $[71, 71, w - 5]$ $-7e^{2} - e + 30$
73 $[73, 73, w^{2} + 2w - 5]$ $\phantom{-}e^{2} + 3e - 5$
73 $[73, 73, 2w^{2} - w - 11]$ $\phantom{-}e^{2} - 2e - 7$
73 $[73, 73, -2w - 1]$ $-2e^{2} - 3e + 7$
83 $[83, 83, 4w^{2} - 31]$ $-3e^{2} + 2e + 15$
97 $[97, 97, 2w^{2} + 2w - 5]$ $-4e^{2} + 29$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w^{2} + 2w - 2]$ $-1$
$4$ $[4, 2, -w^{2} + w + 5]$ $1$