Properties

Label 3.3.1593.1-13.1-b
Base field 3.3.1593.1
Weight $[2, 2, 2]$
Level norm $13$
Level $[13, 13, w^{2} - 3w - 2]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1593.1

Generator \(w\), with minimal polynomial \(x^{3} - 9x - 7\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[13, 13, w^{2} - 3w - 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $32$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 2]$ $\phantom{-}e$
5 $[5, 5, w^{2} - 2w - 4]$ $\phantom{-}\frac{1}{2}e - 1$
7 $[7, 7, w]$ $\phantom{-}3$
7 $[7, 7, w + 3]$ $-e - 1$
7 $[7, 7, -w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{2}e + 2$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{2}e + 3$
13 $[13, 13, w^{2} - 3w - 2]$ $\phantom{-}1$
17 $[17, 17, w - 2]$ $-e + 2$
25 $[25, 5, -w^{2} - w + 3]$ $\phantom{-}0$
29 $[29, 29, w^{2} - 2w - 6]$ $-e + 5$
31 $[31, 31, w^{2} - 5]$ $-\frac{3}{2}e$
37 $[37, 37, -w^{2} - 2w + 2]$ $\phantom{-}3$
41 $[41, 41, w^{2} - 8]$ $-e + 5$
43 $[43, 43, w^{2} - w - 4]$ $-\frac{3}{2}e - 3$
53 $[53, 53, 2w^{2} - 5w - 4]$ $-\frac{3}{2}e - 3$
59 $[59, 59, w^{2} - 3]$ $\phantom{-}2e - 6$
59 $[59, 59, w^{2} - 3w - 5]$ $-e + 4$
61 $[61, 61, -w^{2} + 2w + 12]$ $-\frac{1}{2}e - 8$
67 $[67, 67, -2w^{2} + 6w + 3]$ $\phantom{-}e + 2$
71 $[71, 71, w^{2} - w - 11]$ $-\frac{7}{2}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w^{2} - 3w - 2]$ $-1$