Properties

 Label 4.4.13676.1-16.2-d Base field 4.4.13676.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 4, w^{2} - 3]$ Dimension $3$ CM no Base change no

Related objects

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Base field 4.4.13676.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 6x^{2} + 7x + 1$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 4, w^{2} - 3]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + x^{2} - 7x + 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}0$
4 $[4, 2, -w^{2} - w + 3]$ $\phantom{-}e$
5 $[5, 5, w^{3} - 5w + 1]$ $-\frac{1}{2}e^{2} - e + \frac{3}{2}$
11 $[11, 11, -w^{3} + 6w - 2]$ $-e^{2} + 5$
13 $[13, 13, -w^{2} + 4]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}$
17 $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ $\phantom{-}\frac{1}{2}e^{2} - e - \frac{7}{2}$
37 $[37, 37, w^{3} + w^{2} - 6w - 3]$ $-\frac{1}{2}e^{2} - 2e + \frac{17}{2}$
37 $[37, 37, -w^{3} + 6w - 4]$ $-\frac{5}{2}e^{2} - 3e + \frac{19}{2}$
41 $[41, 41, -w^{3} + 5w - 5]$ $\phantom{-}\frac{3}{2}e^{2} + 4e - \frac{15}{2}$
43 $[43, 43, w^{3} - 4w + 4]$ $-2e^{2} - 4e + 10$
43 $[43, 43, -2w^{3} + 11w - 2]$ $-e^{2} - 2e + 3$
47 $[47, 47, -2w^{3} - w^{2} + 12w]$ $-2e^{2} - 4e + 14$
47 $[47, 47, 2w - 1]$ $\phantom{-}4e + 4$
61 $[61, 61, -w^{3} + w^{2} + 6w - 5]$ $-e^{2} - 5$
71 $[71, 71, w^{3} + w^{2} - 4w - 3]$ $-e^{2} + 1$
71 $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ $-e^{2} - 2e + 7$
79 $[79, 79, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}2e^{2} + 4e - 14$
81 $[81, 3, -3]$ $-\frac{1}{2}e^{2} + 2e + \frac{17}{2}$
83 $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ $-e^{2} + 2e + 15$
97 $[97, 97, w^{3} + w^{2} - 6w + 1]$ $\phantom{-}\frac{5}{2}e^{2} + 3e - \frac{35}{2}$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 1]$ $1$