Properties

Label 4.4.7232.1-17.1-e
Base field 4.4.7232.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, w^{2} - w - 5]$
Dimension $5$
CM no
Base change no

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Base field 4.4.7232.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 4\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, w^{2} - w - 5]$
Dimension: $5$
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:

\(x^{5} + x^{4} - 7x^{3} - 3x^{2} + 11x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 3]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 9e + 7$
17 $[17, 17, w^{2} - w - 5]$ $\phantom{-}1$
17 $[17, 17, -\frac{1}{2}w^{3} + 2w^{2} + \frac{1}{2}w - 2]$ $\phantom{-}e^{2} - 8$
23 $[23, 23, \frac{1}{2}w^{3} - 2w^{2} - \frac{1}{2}w + 4]$ $\phantom{-}e^{4} - e^{3} - 8e^{2} + 4e + 8$
23 $[23, 23, -w^{2} + w + 3]$ $-4e^{4} - 6e^{3} + 23e^{2} + 23e - 24$
41 $[41, 41, -w^{3} + 3w^{2} + 2w - 7]$ $\phantom{-}4e^{4} + 5e^{3} - 23e^{2} - 20e + 20$
41 $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w]$ $\phantom{-}e^{4} - 5e^{2} + e - 4$
41 $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ $\phantom{-}2e^{4} + 4e^{3} - 11e^{2} - 15e + 14$
41 $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w]$ $\phantom{-}e^{4} + 3e^{3} - 5e^{2} - 14e + 4$
47 $[47, 47, \frac{3}{2}w^{3} - 4w^{2} - \frac{7}{2}w + 6]$ $-6e^{4} - 10e^{3} + 37e^{2} + 44e - 40$
47 $[47, 47, w^{3} - w^{2} - 4w - 1]$ $\phantom{-}6e^{4} + 11e^{3} - 35e^{2} - 43e + 38$
49 $[49, 7, w^{3} - 2w^{2} - 3w + 1]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 10e + 6$
49 $[49, 7, \frac{1}{2}w^{3} - w^{2} - \frac{3}{2}w - 2]$ $-6e^{4} - 12e^{3} + 34e^{2} + 49e - 42$
71 $[71, 71, \frac{5}{2}w^{3} - 6w^{2} - \frac{17}{2}w + 12]$ $\phantom{-}e^{4} + 3e^{3} - 9e^{2} - 14e + 16$
71 $[71, 71, 2w^{2} - 4w - 7]$ $\phantom{-}4e^{4} + 7e^{3} - 26e^{2} - 32e + 32$
73 $[73, 73, -w^{3} + 2w^{2} + 5w - 3]$ $-7e^{4} - 10e^{3} + 37e^{2} + 38e - 34$
73 $[73, 73, 2w - 1]$ $\phantom{-}3e^{4} + 6e^{3} - 22e^{2} - 30e + 32$
79 $[79, 79, \frac{3}{2}w^{3} - 4w^{2} - \frac{11}{2}w + 12]$ $-5e^{4} - 10e^{3} + 32e^{2} + 43e - 42$
79 $[79, 79, -w^{2} - w - 1]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, w^{2} - w - 5]$ $-1$