Properties

Label 4.4.10309.1-9.1-c
Base field 4.4.10309.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{3} - 5w + 3]$
Dimension $5$
CM no
Base change yes

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Base field 4.4.10309.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 8x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 3, w^{3} - 5w + 3]$
Dimension: $5$
CM: no
Base change: yes
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 10x^{4} + 20x^{3} + 40x^{2} - 80x - 80\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, w^{3} - 5w + 3]$ $-1$
9 $[9, 3, w^{3} - 5w + 2]$ $\phantom{-}e$
13 $[13, 13, w + 1]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{3}{4}e^{3} - \frac{1}{2}e^{2} + 3e + 4$
13 $[13, 13, w^{3} - 6w + 4]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{3}{4}e^{3} - \frac{1}{2}e^{2} + 3e + 4$
16 $[16, 2, 2]$ $-\frac{1}{4}e^{4} + \frac{9}{4}e^{3} - \frac{7}{2}e^{2} - 6e + 7$
17 $[17, 17, w^{2} + w - 2]$ $-\frac{1}{8}e^{4} + \frac{3}{4}e^{3} + e^{2} - 6e - 2$
17 $[17, 17, w^{2} + w - 5]$ $-\frac{1}{8}e^{4} + \frac{3}{4}e^{3} + e^{2} - 6e - 2$
23 $[23, 23, w^{3} - w^{2} - 6w + 6]$ $-\frac{1}{4}e^{3} + \frac{3}{2}e^{2} + e - 6$
23 $[23, 23, w^{3} + w^{2} - 4w - 1]$ $-\frac{1}{4}e^{3} + \frac{3}{2}e^{2} + e - 6$
25 $[25, 5, -w^{2} + 3]$ $-\frac{1}{4}e^{4} + 2e^{3} - \frac{5}{2}e^{2} - 5e + 6$
25 $[25, 5, -w^{3} - w^{2} + 5w + 1]$ $-\frac{1}{4}e^{4} + 2e^{3} - \frac{5}{2}e^{2} - 5e + 6$
29 $[29, 29, -w^{2} - 2w + 3]$ $\phantom{-}\frac{1}{4}e^{4} - 2e^{3} + 2e^{2} + 7e$
29 $[29, 29, -w^{3} + w^{2} + 7w - 7]$ $\phantom{-}\frac{1}{4}e^{4} - 2e^{3} + 2e^{2} + 7e$
43 $[43, 43, 2w^{3} + w^{2} - 10w + 3]$ $-\frac{1}{2}e^{3} + 3e^{2} - e - 6$
43 $[43, 43, -w^{3} + w^{2} + 5w - 7]$ $-\frac{1}{2}e^{3} + 3e^{2} - e - 6$
53 $[53, 53, w^{3} - w^{2} - 7w + 5]$ $-\frac{1}{2}e^{3} + 5e^{2} - 8e - 16$
53 $[53, 53, w^{2} + 2w - 5]$ $-\frac{1}{2}e^{3} + 5e^{2} - 8e - 16$
61 $[61, 61, 2w^{3} + w^{2} - 10w]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e^{2} + 7e + 12$
61 $[61, 61, w^{3} - 7w + 3]$ $-\frac{1}{4}e^{4} + \frac{5}{2}e^{3} - 5e^{2} - 10e + 12$
61 $[61, 61, 2w^{3} + w^{2} - 9w + 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e^{2} + 7e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, w^{3} - 5w + 3]$ $1$