Properties

Label 6.6.1997632.1-13.1-f
Base field 6.6.1997632.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, w]$
Dimension $4$
CM no
Base change no

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Base field 6.6.1997632.1

Generator \(w\), with minimal polynomial \(x^{6} - 8x^{4} + 19x^{2} - 13\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[13, 13, w]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 44x^{2} + 324\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
8 $[8, 2, w^{4} - 5w^{2} - w + 4]$ $\phantom{-}0$
13 $[13, 13, w]$ $-1$
13 $[13, 13, -w^{2} + w + 3]$ $-\frac{1}{12}e^{3} + \frac{13}{6}e$
13 $[13, 13, w^{2} + w - 3]$ $\phantom{-}\frac{1}{12}e^{3} - \frac{13}{6}e$
27 $[27, 3, w^{5} - 6w^{3} + w^{2} + 8w - 2]$ $\phantom{-}2$
27 $[27, 3, w^{5} - 6w^{3} - w^{2} + 8w + 2]$ $\phantom{-}2$
29 $[29, 29, w^{4} - 6w^{2} + w + 8]$ $\phantom{-}e$
29 $[29, 29, -w^{4} + 6w^{2} + w - 8]$ $-e$
41 $[41, 41, w^{3} - w^{2} - 3w + 4]$ $-\frac{1}{2}e^{2} + 15$
41 $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{16}{3}e$
41 $[41, 41, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 3]$ $-\frac{1}{6}e^{3} + \frac{16}{3}e$
41 $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 8w - 6]$ $-\frac{1}{2}e^{2} + 15$
43 $[43, 43, -w^{4} + 6w^{2} - w - 9]$ $\phantom{-}2e$
43 $[43, 43, -w^{4} + 6w^{2} + w - 9]$ $-2e$
49 $[49, 7, w^{4} - 5w^{2} + 7]$ $-4$
97 $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 4]$ $-e$
97 $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 3]$ $-\frac{1}{12}e^{3} + \frac{1}{6}e$
97 $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $\phantom{-}\frac{1}{12}e^{3} - \frac{1}{6}e$
97 $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ $\phantom{-}e$
113 $[113, 113, w^{5} - w^{4} - 6w^{3} + 6w^{2} + 7w - 9]$ $\phantom{-}\frac{1}{12}e^{3} - \frac{1}{6}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w]$ $1$