Properties

Label 4.4.18097.1-16.1-a
Base field 4.4.18097.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $3$
CM no
Base change no

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Base field 4.4.18097.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - x^{2} - 2x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}e$
4 $[4, 2, w]$ $\phantom{-}1$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $-1$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $-2e^{2} + 2$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $\phantom{-}2e - 2$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $-e^{2} + 2e + 2$
27 $[27, 3, -w^{3} + 7w + 1]$ $\phantom{-}4e^{2} - 3e - 6$
31 $[31, 31, w + 3]$ $\phantom{-}4e^{2} - 2e - 10$
31 $[31, 31, -w^{2} + 5]$ $-2e^{2} + 8$
37 $[37, 37, w^{2} - 3]$ $-2$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $\phantom{-}e^{2} + 5e - 3$
47 $[47, 47, w^{3} - 5w - 3]$ $-6e^{2} + 6$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $\phantom{-}2e^{2} - 4e - 6$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $\phantom{-}6e^{2} - 6e - 10$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $-3e^{2} - 3e + 1$
83 $[83, 83, -w^{3} + 5w + 1]$ $\phantom{-}3e^{2} + 4e$
83 $[83, 83, 2w - 1]$ $\phantom{-}5e^{2} - 5e - 7$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $\phantom{-}4e^{2} - 9e - 12$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $-3e^{2}$
89 $[89, 89, w^{3} - 5w + 5]$ $-11e^{2} - e + 21$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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