Properties

 Label 4.4.19025.1-16.3-a Base field 4.4.19025.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16,4,w^{2} - 2w - 7]$ Dimension $14$ CM no Base change no

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Base field 4.4.19025.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 13x^{2} + 14x + 44$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[16,4,w^{2} - 2w - 7]$ Dimension: $14$ 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:

 $$x^{14} - 3x^{13} - 32x^{12} + 102x^{11} + 330x^{10} - 1156x^{9} - 1253x^{8} + 5179x^{7} + 1948x^{6} - 9758x^{5} - 2037x^{4} + 7016x^{3} + 1988x^{2} - 820x - 85$$
Norm Prime Eigenvalue
4 $[4, 2, w^{2} - 2w - 6]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + 7]$ $\phantom{-}0$
5 $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $...$
5 $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $...$
11 $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ $...$
11 $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ $...$
31 $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ $...$
31 $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $...$
41 $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ $...$
41 $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ $...$
41 $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ $...$
41 $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ $...$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ $...$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $...$
71 $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ $...$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ $...$
81 $[81, 3, -3]$ $...$
89 $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ $...$
89 $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ $...$
89 $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ $...$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,w^{2} - 7]$ $1$