Properties

Label 4.4.10273.1-16.2-e
Base field 4.4.10273.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 16, -w + 2]$
Dimension $2$
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: $[16, 16, -w + 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 4x - 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}0$
3 $[3, 3, w - 1]$ $\phantom{-}0$
8 $[8, 2, w^{3} - 2w^{2} - 5w + 1]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 2w + 3]$ $\phantom{-}e - 3$
17 $[17, 17, -w^{2} + 3w + 3]$ $\phantom{-}e - 3$
17 $[17, 17, -w^{2} + 2w + 1]$ $-e - 1$
27 $[27, 3, w^{3} - w^{2} - 6w - 5]$ $-4$
29 $[29, 29, w^{3} - 2w^{2} - 2w + 1]$ $\phantom{-}e - 7$
47 $[47, 47, w^{3} - 2w^{2} - 4w - 3]$ $-2e + 2$
49 $[49, 7, w^{3} - 3w^{2} - 3w + 1]$ $\phantom{-}3e - 5$
49 $[49, 7, -2w^{3} + 5w^{2} + 7w - 3]$ $-2e + 8$
59 $[59, 59, -2w^{3} + 6w^{2} + 5w - 7]$ $\phantom{-}0$
61 $[61, 61, 2w^{3} - 4w^{2} - 9w - 3]$ $\phantom{-}e - 3$
71 $[71, 71, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}12$
73 $[73, 73, 2w^{3} - 6w^{2} - 3w + 5]$ $\phantom{-}2$
73 $[73, 73, w^{3} - 3w^{2} - 4w + 5]$ $-e + 11$
83 $[83, 83, -2w^{3} + 5w^{2} + 8w - 3]$ $\phantom{-}12$
89 $[89, 89, -2w^{3} + 6w^{2} + 4w - 7]$ $\phantom{-}2e - 4$
89 $[89, 89, w^{3} - 2w^{2} - 6w + 3]$ $\phantom{-}2e - 4$
97 $[97, 97, -3w - 1]$ $-3e + 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w]$ $1$