Properties

Label 4.4.12357.1-21.2-d
Base field 4.4.12357.1
Weight $[2, 2, 2, 2]$
Level norm $21$
Level $[21, 21, -w + 3]$
Dimension $2$
CM no
Base change no

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Base field 4.4.12357.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[21, 21, -w + 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
3 $[3, 3, w + 1]$ $\phantom{-}0$
7 $[7, 7, -w^{2} + 2]$ $-1$
11 $[11, 11, -w^{2} - w + 1]$ $\phantom{-}0$
16 $[16, 2, 2]$ $\phantom{-}1$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}e$
19 $[19, 19, -w^{3} + w^{2} + 5w - 2]$ $-4$
23 $[23, 23, -w^{3} + w^{2} + 3w - 4]$ $-2e$
31 $[31, 31, w^{3} - w^{2} - 3w + 1]$ $-8$
41 $[41, 41, -w^{3} + 4w - 1]$ $-e$
43 $[43, 43, w^{3} + w^{2} - 5w - 4]$ $-4$
53 $[53, 53, w^{3} - w^{2} - 4w - 1]$ $-e$
53 $[53, 53, -w^{2} - w + 4]$ $\phantom{-}e$
59 $[59, 59, -w^{3} + 4w - 2]$ $\phantom{-}2e$
67 $[67, 67, -2w^{3} + w^{2} + 8w + 1]$ $-4$
89 $[89, 89, -2w^{3} + 3w^{2} + 8w - 8]$ $\phantom{-}3e$
89 $[89, 89, w^{3} - 5w + 1]$ $\phantom{-}5e$
97 $[97, 97, w^{3} - 6w - 1]$ $\phantom{-}10$
97 $[97, 97, -w^{3} + 3w^{2} + 4w - 10]$ $\phantom{-}10$
101 $[101, 101, -w^{3} + 6w - 2]$ $-3e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $1$
$7$ $[7, 7, -w^{2} + 2]$ $1$