Properties

Label 4.4.10309.1-13.2-d
Base field 4.4.10309.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13,13,w^{3} - 6w + 4]$
Dimension $3$
CM no
Base change no

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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: $[13,13,w^{3} - 6w + 4]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + 2x^{2} - 16x - 20\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, w^{3} - 5w + 3]$ $\phantom{-}e$
9 $[9, 3, w^{3} - 5w + 2]$ $\phantom{-}2$
13 $[13, 13, w + 1]$ $-e + 2$
13 $[13, 13, w^{3} - 6w + 4]$ $-1$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{2} + 5$
17 $[17, 17, w^{2} + w - 2]$ $-e$
17 $[17, 17, w^{2} + w - 5]$ $\phantom{-}3$
23 $[23, 23, w^{3} - w^{2} - 6w + 6]$ $-e + 4$
23 $[23, 23, w^{3} + w^{2} - 4w - 1]$ $-e + 4$
25 $[25, 5, -w^{2} + 3]$ $\phantom{-}e + 2$
25 $[25, 5, -w^{3} - w^{2} + 5w + 1]$ $\phantom{-}e + 2$
29 $[29, 29, -w^{2} - 2w + 3]$ $-\frac{1}{2}e^{2} + e + 9$
29 $[29, 29, -w^{3} + w^{2} + 7w - 7]$ $\phantom{-}\frac{1}{2}e^{2} - 2e - 9$
43 $[43, 43, 2w^{3} + w^{2} - 10w + 3]$ $\phantom{-}e^{2} + e - 11$
43 $[43, 43, -w^{3} + w^{2} + 5w - 7]$ $-\frac{1}{2}e^{2} + 9$
53 $[53, 53, w^{3} - w^{2} - 7w + 5]$ $\phantom{-}e^{2} - 10$
53 $[53, 53, w^{2} + 2w - 5]$ $\phantom{-}e + 2$
61 $[61, 61, 2w^{3} + w^{2} - 10w]$ $-e^{2} - e + 5$
61 $[61, 61, w^{3} - 7w + 3]$ $-\frac{1}{2}e^{2} - e - 1$
61 $[61, 61, 2w^{3} + w^{2} - 9w + 3]$ $-1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13,13,w^{3} - 6w + 4]$ $1$