Properties

 Label 4.4.17600.1-16.1-b Base field 4.4.17600.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $2$ CM no Base change no

Related objects

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Base field 4.4.17600.1

Generator $$w$$, with minimal polynomial $$x^{4} - 14x^{2} + 44$$; narrow class number $$2$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 2x - 4$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ $\phantom{-}0$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ $-2$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $\phantom{-}e$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $\phantom{-}e - 4$
19 $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ $-e$
19 $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ $-2e - 2$
19 $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ $\phantom{-}2e - 2$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ $\phantom{-}3e - 4$
25 $[25, 5, \frac{1}{2}w^{2} - 1]$ $-2$
29 $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ $\phantom{-}2e + 4$
29 $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ $-2e + 4$
31 $[31, 31, -w - 1]$ $-4$
31 $[31, 31, w - 1]$ $-4e + 4$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ $\phantom{-}2$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ $-2e + 10$
49 $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ $-2e - 2$
49 $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ $-4e + 6$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ $-2e - 2$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ $-2e - 2$
61 $[61, 61, \frac{1}{2}w^{2} + w - 6]$ $\phantom{-}5e - 2$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ $-1$