Properties

Label 3.3.961.1-16.11-e
Base field 3.3.961.1
Weight $[2, 2, 2]$
Level norm $16$
Level $[16,8,-w + 4]$
Dimension $1$
CM no
Base change no

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Base field 3.3.961.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 8\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[16,8,-w + 4]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{2} - \frac{1}{2}w - 4]$ $\phantom{-}0$
2 $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 3]$ $-1$
2 $[2, 2, -w + 1]$ $\phantom{-}2$
23 $[23, 23, -w^{2} + w + 7]$ $-3$
23 $[23, 23, w^{2} + w - 7]$ $-3$
23 $[23, 23, -2w + 1]$ $\phantom{-}0$
27 $[27, 3, 3]$ $-7$
29 $[29, 29, -w^{2} - 3w + 1]$ $-9$
29 $[29, 29, w^{2} - 3w + 1]$ $\phantom{-}0$
29 $[29, 29, -2w^{2} + 21]$ $-7$
31 $[31, 31, -3w^{2} + w + 31]$ $\phantom{-}4$
47 $[47, 47, 2w - 3]$ $\phantom{-}11$
47 $[47, 47, w^{2} + w - 5]$ $-9$
47 $[47, 47, w^{2} - w - 9]$ $-8$
61 $[61, 61, w^{2} - w - 11]$ $-10$
61 $[61, 61, -w^{2} - w + 3]$ $-7$
61 $[61, 61, -2w + 5]$ $-2$
89 $[89, 89, w^{2} - w - 1]$ $-1$
89 $[89, 89, w^{2} + w - 13]$ $\phantom{-}4$
89 $[89, 89, -2w - 5]$ $-10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,-\frac{1}{2}w^{2} - \frac{1}{2}w + 3]$ $1$
$2$ $[2,2,-\frac{1}{2}w^{2} + \frac{1}{2}w + 4]$ $1$