Properties

Label 4.4.19225.1-16.1-f
Base field 4.4.19225.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $4$
CM no
Base change no

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Base field 4.4.19225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $29$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 2x^{3} - 17x^{2} - 21x + 70\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}1$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $-1$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $-e$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $\phantom{-}e^{3} - e^{2} - 11e + 14$
11 $[11, 11, -w - 3]$ $-e^{3} + e^{2} + 11e - 16$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $-e^{3} + 2e^{2} + 12e - 24$
29 $[29, 29, w + 1]$ $-e^{3} + 3e^{2} + 13e - 30$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $-e^{3} + e^{2} + 11e - 20$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $-e + 4$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $\phantom{-}e^{3} - e^{2} - 12e + 14$
31 $[31, 31, -w + 3]$ $\phantom{-}e^{3} - 3e^{2} - 12e + 34$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $-2e^{2} - e + 14$
59 $[59, 59, 2w^{2} - w - 13]$ $-2e^{3} + 4e^{2} + 24e - 50$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $\phantom{-}2e$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $\phantom{-}2e^{3} - 4e^{2} - 26e + 44$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-6$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $-e^{3} + 2e^{2} + 15e - 26$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $\phantom{-}3e^{3} - 4e^{2} - 35e + 54$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $\phantom{-}e^{3} - 2e^{2} - 12e + 20$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, w + 2]$ $-1$
$4$ $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $1$