Properties

Label 4.4.14013.1-1.1-c
Base field 4.4.14013.1
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 4.4.14013.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 6x + 3\); 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: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 10\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}0$
3 $[3, 3, w - 1]$ $\phantom{-}e$
7 $[7, 7, w + 1]$ $\phantom{-}2$
7 $[7, 7, -w^{3} + 5w - 2]$ $-e$
13 $[13, 13, -w^{3} + 5w + 1]$ $-e$
16 $[16, 2, 2]$ $\phantom{-}5$
29 $[29, 29, w^{3} + w^{2} - 5w - 1]$ $\phantom{-}3e$
31 $[31, 31, -w^{3} + 4w - 1]$ $\phantom{-}2e$
41 $[41, 41, w^{3} - 6w + 1]$ $\phantom{-}0$
43 $[43, 43, w^{3} + w^{2} - 6w - 1]$ $-e$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 11]$ $-12$
49 $[49, 7, w^{2} + w - 1]$ $-4e$
59 $[59, 59, w^{3} - w^{2} - 6w + 4]$ $-3e$
59 $[59, 59, w^{2} - w - 4]$ $-6$
67 $[67, 67, 2w^{3} + w^{2} - 9w - 2]$ $-4e$
71 $[71, 71, -3w^{3} - w^{2} + 16w + 5]$ $\phantom{-}0$
71 $[71, 71, 2w - 1]$ $-3e$
73 $[73, 73, w^{3} - 6w + 4]$ $-e$
83 $[83, 83, w^{3} - w^{2} - 3w + 4]$ $\phantom{-}6$
103 $[103, 103, w^{3} + w^{2} - 4w - 5]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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