Properties

Label 4.4.19773.1-9.3-c
Base field 4.4.19773.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9,3,-w^{3} + 3w^{2} + 6w - 4]$
Dimension $4$
CM no
Base change yes

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Base field 4.4.19773.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} - 9x + 3\); narrow class number \(4\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[9,3,-w^{3} + 3w^{2} + 6w - 4]$
Dimension: $4$
CM: no
Base change: yes
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 128x^{2} + 1936\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{3} - 2w^{2} - 8w - 3]$ $\phantom{-}\frac{1}{88}e^{3} - \frac{21}{22}e$
3 $[3, 3, w^{3} - 3w^{2} - 5w + 2]$ $\phantom{-}0$
13 $[13, 13, w^{3} - 2w^{2} - 6w + 1]$ $\phantom{-}\frac{1}{44}e^{3} - \frac{21}{11}e$
16 $[16, 2, 2]$ $\phantom{-}5$
17 $[17, 17, -2w^{3} + 5w^{2} + 14w - 1]$ $\phantom{-}0$
17 $[17, 17, -w^{3} + 3w^{2} + 5w - 4]$ $\phantom{-}\frac{1}{88}e^{3} - \frac{43}{22}e$
17 $[17, 17, -w^{3} + 2w^{2} + 8w + 1]$ $\phantom{-}0$
17 $[17, 17, w - 1]$ $\phantom{-}\frac{1}{88}e^{3} - \frac{43}{22}e$
23 $[23, 23, 2w^{3} - 6w^{2} - 11w + 7]$ $-\frac{1}{264}e^{3} + \frac{43}{66}e$
23 $[23, 23, w^{3} - 3w^{2} - 7w + 4]$ $-\frac{1}{264}e^{3} + \frac{43}{66}e$
23 $[23, 23, -w^{2} + 2w + 5]$ $\phantom{-}\frac{1}{6}e^{2} - \frac{32}{3}$
23 $[23, 23, 3w^{3} - 8w^{2} - 20w + 5]$ $\phantom{-}\frac{1}{6}e^{2} - \frac{32}{3}$
61 $[61, 61, -w^{3} + 2w^{2} + 9w + 1]$ $-\frac{1}{88}e^{3} + \frac{21}{22}e$
61 $[61, 61, -2w^{3} + 5w^{2} + 13w - 2]$ $-\frac{1}{88}e^{3} + \frac{21}{22}e$
61 $[61, 61, w^{3} - 2w^{2} - 9w - 2]$ $-\frac{1}{88}e^{3} + \frac{21}{22}e$
61 $[61, 61, 2w^{3} - 5w^{2} - 13w + 1]$ $-\frac{1}{88}e^{3} + \frac{21}{22}e$
79 $[79, 79, 4w^{3} - 10w^{2} - 28w + 5]$ $-\frac{1}{22}e^{3} + \frac{42}{11}e$
79 $[79, 79, w^{3} - 3w^{2} - 4w + 4]$ $-\frac{1}{22}e^{3} + \frac{42}{11}e$
79 $[79, 79, w^{3} - 4w^{2} - 2w + 10]$ $-\frac{1}{88}e^{3} + \frac{21}{22}e$
79 $[79, 79, 2w^{3} - 6w^{2} - 10w + 5]$ $-\frac{1}{88}e^{3} + \frac{21}{22}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3,3,w^{3} - 3w^{2} - 5w + 2]$ $1$