Properties

Label 4.4.19429.1-1.1-a
Base field 4.4.19429.1
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 4.4.19429.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}2$
5 $[5, 5, w]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}4$
13 $[13, 13, -w^{2} + w + 4]$ $-e + 1$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $-e - 1$
16 $[16, 2, 2]$ $\phantom{-}2e + 1$
17 $[17, 17, -w + 2]$ $-e - 3$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-2e - 2$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $-2e - 4$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}2e + 2$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}4$
41 $[41, 41, w^{2} - w - 1]$ $\phantom{-}e - 6$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $\phantom{-}10$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $\phantom{-}6$
53 $[53, 53, -w - 3]$ $\phantom{-}e - 6$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $\phantom{-}e + 6$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-6$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $-2e$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $-10$
79 $[79, 79, w^{2} - 2w - 1]$ $\phantom{-}2e + 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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