Properties

Label 4.4.10273.1-17.2-a
Base field 4.4.10273.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, -w^{2} + 2w + 1]$
Dimension $4$
CM no
Base change no

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Base field 4.4.10273.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, -w^{2} + 2w + 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $21$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 3x^{3} - 4x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $\phantom{-}e^{3} + e^{2} - 2e$
8 $[8, 2, w^{3} - 2w^{2} - 5w + 1]$ $-e^{3} - 3e^{2} + 2$
13 $[13, 13, -w^{2} + 2w + 3]$ $\phantom{-}e^{2} - 3$
17 $[17, 17, -w^{2} + 3w + 3]$ $\phantom{-}e^{3} + 2e^{2} - 2e - 3$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}1$
27 $[27, 3, w^{3} - w^{2} - 6w - 5]$ $\phantom{-}5e^{2} + 6e - 8$
29 $[29, 29, w^{3} - 2w^{2} - 2w + 1]$ $-2e^{3} - 4e^{2} + 5e + 7$
47 $[47, 47, w^{3} - 2w^{2} - 4w - 3]$ $\phantom{-}3e^{3} + 3e^{2} - 6e$
49 $[49, 7, w^{3} - 3w^{2} - 3w + 1]$ $-5e^{3} - 12e^{2} + 3e + 9$
49 $[49, 7, -2w^{3} + 5w^{2} + 7w - 3]$ $\phantom{-}2e^{3} - 7e$
59 $[59, 59, -2w^{3} + 6w^{2} + 5w - 7]$ $-2e^{3} + 11e - 2$
61 $[61, 61, 2w^{3} - 4w^{2} - 9w - 3]$ $-8e^{3} - 15e^{2} + 12e + 12$
71 $[71, 71, w^{3} - 3w^{2} - 3w + 7]$ $-3e^{3} - 7e^{2} + e + 10$
73 $[73, 73, 2w^{3} - 6w^{2} - 3w + 5]$ $\phantom{-}6e^{3} + 16e^{2} - 5e - 15$
73 $[73, 73, w^{3} - 3w^{2} - 4w + 5]$ $\phantom{-}9e^{3} + 21e^{2} - 7e - 15$
83 $[83, 83, -2w^{3} + 5w^{2} + 8w - 3]$ $\phantom{-}3e^{3} + 4e^{2} - 5e - 6$
89 $[89, 89, -2w^{3} + 6w^{2} + 4w - 7]$ $-3e^{3} + 13e - 4$
89 $[89, 89, w^{3} - 2w^{2} - 6w + 3]$ $\phantom{-}5e^{3} + 13e^{2} - 3e - 18$
97 $[97, 97, -3w - 1]$ $-4e^{3} - 8e^{2} + e + 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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