Properties

 Label 4.4.12400.1-16.1-c Base field 4.4.12400.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $4$ CM no Base change no

Related objects

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Base field 4.4.12400.1

Generator $$w$$, with minimal polynomial $$x^{4} - 12x^{2} + 31$$; narrow class number $$2$$ and class number $$1$$.

Form

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

Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 6x^{2} + 4$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ $\phantom{-}0$
5 $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ $-e$
5 $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ $\phantom{-}e^{3} - 5e$
9 $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ $-e^{3} + 5e$
19 $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ $-2e^{3} + 10e$
19 $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ $\phantom{-}2e^{3} - 10e$
29 $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ $\phantom{-}e^{2} - 6$
29 $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ $\phantom{-}e^{2} - 6$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $\phantom{-}0$
59 $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ $-2e^{2} + 4$
59 $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ $-2e^{2} + 4$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ $-3e^{3} + 13e$
61 $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ $\phantom{-}3e^{3} - 13e$
71 $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ $\phantom{-}4e^{3} - 18e$
71 $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ $-4e^{3} + 18e$
79 $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ $\phantom{-}2e^{3} - 10e$
79 $[79, 79, -2w^{2} + w + 10]$ $-4e^{2} + 8$
79 $[79, 79, 2w^{2} + w - 10]$ $-4e^{2} + 8$
79 $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ $-2e^{3} + 10e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,-\frac{1}{2}w^{3}-\frac{1}{2}w^{2}+\frac{7}{2}w+\frac{11}{2}]$ $-1$