Properties

Label 4.4.19796.1-1.1-a
Base field 4.4.19796.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $4$
CM yes
Base change no

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Base field 4.4.19796.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $4$
CM: yes
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 2x^{3} - 8x^{2} + 16x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2]$ $\phantom{-}e$
2 $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{7}{2}e - \frac{5}{2}$
5 $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}0$
13 $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ $\phantom{-}0$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}0$
19 $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ $\phantom{-}0$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $-e^{3} + 7e - 6$
31 $[31, 31, -w^{2} + w + 1]$ $\phantom{-}0$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}0$
49 $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ $\phantom{-}0$
53 $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ $\phantom{-}3e^{3} + 2e^{2} - 23e$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}4e^{3} - 30e + 12$
61 $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ $\phantom{-}0$
61 $[61, 61, 2w^{2} - 7]$ $\phantom{-}0$
71 $[71, 71, w^{2} - 3w - 5]$ $-3e^{3} - 4e^{2} + 21e + 18$
73 $[73, 73, 2w - 3]$ $\phantom{-}0$
73 $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ $\phantom{-}0$
79 $[79, 79, 2w^{2} - 5]$ $\phantom{-}e^{3} - 2e^{2} - 3e + 12$
81 $[81, 3, -3]$ $\phantom{-}6e$
101 $[101, 101, 2w^{2} - 4w - 9]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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