Properties

Label 4.4.15529.1-1.1-b
Base field 4.4.15529.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $2$
CM no
Base change no

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Base field 4.4.15529.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 2x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}e + 3$
8 $[8, 2, -w^{3} + w^{2} + 6w + 1]$ $-e - 2$
9 $[9, 3, -w^{3} + w^{2} + 5w + 1]$ $\phantom{-}2e + 4$
9 $[9, 3, -w^{3} + 2w^{2} + 3w - 1]$ $-e - 1$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}2e$
23 $[23, 23, w^{2} - 2w - 1]$ $-4e - 6$
29 $[29, 29, w^{2} - 3w - 1]$ $\phantom{-}e - 1$
29 $[29, 29, -w^{2} + w + 3]$ $\phantom{-}3e + 7$
37 $[37, 37, w^{3} - w^{2} - 5w + 1]$ $\phantom{-}10$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}2$
47 $[47, 47, -w^{2} + 2w + 5]$ $-6e - 4$
47 $[47, 47, 2w^{3} - 2w^{2} - 11w - 5]$ $-4e - 10$
53 $[53, 53, -w^{3} + 2w^{2} + 2w + 1]$ $\phantom{-}2e + 6$
59 $[59, 59, -w - 3]$ $-6e - 6$
73 $[73, 73, w^{2} - w + 1]$ $\phantom{-}e + 1$
73 $[73, 73, 2w^{3} - 2w^{2} - 12w - 5]$ $\phantom{-}e + 15$
79 $[79, 79, 4w^{3} - 4w^{2} - 22w - 7]$ $-6e$
97 $[97, 97, 2w^{3} - 3w^{2} - 9w + 1]$ $-e + 3$
101 $[101, 101, 2w^{2} - 2w - 9]$ $-3e - 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).