Properties

Label 4.4.19225.1-16.3-d
Base field 4.4.19225.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16,4,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{5}{2}w + 8]$
Dimension $5$
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: $[16,4,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{5}{2}w + 8]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $26$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 8x^{3} - 4x^{2} + 6x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}0$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $\phantom{-}2e^{4} - 15e^{2} - 8e + 7$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $-e^{4} + 7e^{2} + 5e - 1$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $-2e^{4} - 2e^{3} + 18e^{2} + 21e - 11$
11 $[11, 11, -w - 3]$ $-e^{4} + 7e^{2} + 6e$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $\phantom{-}e^{4} + e^{3} - 10e^{2} - 9e + 9$
29 $[29, 29, w + 1]$ $\phantom{-}e^{4} - e^{3} - 6e^{2} + e + 5$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $\phantom{-}e^{4} - 8e^{2} - 7e + 8$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $-2e^{4} + 15e^{2} + 8e - 5$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $-3e^{4} + e^{3} + 22e^{2} + 10e - 10$
31 $[31, 31, -w + 3]$ $\phantom{-}4e^{4} - 30e^{2} - 19e + 11$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $-e^{4} - e^{3} + 7e^{2} + 11e$
59 $[59, 59, 2w^{2} - w - 13]$ $-e^{3} + e^{2} + 5e - 11$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $\phantom{-}e + 5$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $\phantom{-}2e^{4} + 2e^{3} - 16e^{2} - 24e + 2$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-4e^{4} + 30e^{2} + 22e - 10$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $\phantom{-}3e^{4} - 22e^{2} - 14e + 9$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $\phantom{-}2e^{4} - 16e^{2} - 10e + 12$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $\phantom{-}2e^{4} + e^{3} - 17e^{2} - 13e + 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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