Properties

Label 4.4.15188.1-16.3-b
Base field 4.4.15188.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 4, w^{2} - 2w - 3]$
Dimension $2$
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: $[16, 4, w^{2} - 2w - 3]$
Dimension: $2$
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:

\(x^{2} - x - 1\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

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