# Properties

 Label 4.4.15188.1-16.1-d Base field 4.4.15188.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $1$ CM no Base change no

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## Base field 4.4.15188.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + x + 2$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
2 $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ $\phantom{-}0$
11 $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ $-6$
11 $[11, 11, -w^{3} + w^{2} + 6w + 1]$ $-2$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $\phantom{-}0$
19 $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ $-4$
23 $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ $-4$
31 $[31, 31, -w^{3} + w^{2} + 6w - 1]$ $\phantom{-}10$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $\phantom{-}2$
43 $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ $\phantom{-}8$
67 $[67, 67, w^{2} - w - 5]$ $-12$
67 $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ $-12$
73 $[73, 73, w^{2} + w + 1]$ $-6$
79 $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ $-2$
81 $[81, 3, -3]$ $\phantom{-}8$
83 $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ $\phantom{-}14$
83 $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ $\phantom{-}16$
89 $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ $\phantom{-}10$
89 $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ $-8$
97 $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ $-2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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