Properties

Label 4.4.17609.1-1.1-a
Base field 4.4.17609.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $6$
CM no
Base change no

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Base field 4.4.17609.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 8x^{4} + 10x^{2} - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $\phantom{-}e^{4} - 7e^{2} + 5$
7 $[7, 7, -w^{3} + 6w - 2]$ $-e^{5} + 8e^{3} - 11e$
8 $[8, 2, w^{3} - 7w + 3]$ $\phantom{-}e^{3} - 6e$
11 $[11, 11, -w^{3} + 6w - 4]$ $\phantom{-}2e^{5} - 16e^{3} + 20e$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $\phantom{-}1$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}3e^{5} - 23e^{3} + 21e$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $-4e^{5} + 30e^{3} - 26e$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $\phantom{-}2e^{5} - 15e^{3} + 14e$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}2e^{5} - 17e^{3} + 22e$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $-e^{4} + 7e^{2} - 2$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $-e^{5} + 8e^{3} - 9e$
59 $[59, 59, -2w^{3} + 13w - 6]$ $-e^{5} + 10e^{3} - 23e$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $\phantom{-}2e^{4} - 12e^{2} + 6$
59 $[59, 59, w^{2} + w - 1]$ $-4e^{5} + 30e^{3} - 28e$
59 $[59, 59, w^{2} + 2w - 6]$ $-e^{4} + 9e^{2} - 8$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $-e^{5} + 7e^{3} - e$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $\phantom{-}0$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $-5e^{5} + 38e^{3} - 37e$
81 $[81, 3, -3]$ $-2e^{4} + 16e^{2} - 19$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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