Properties

Label 3.3.1929.1-8.1-c
Base field 3.3.1929.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 2, 2]$
Dimension $6$
CM no
Base change no

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Base field 3.3.1929.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[8, 2, 2]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $34$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 15x^{4} + 53x^{2} - 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}1$
3 $[3, 3, w - 1]$ $\phantom{-}e$
7 $[7, 7, w^{2} + w - 7]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 11]$ $\phantom{-}e^{2} - 5$
7 $[7, 7, -w^{2} + 9]$ $\phantom{-}e$
8 $[8, 2, 2]$ $\phantom{-}1$
13 $[13, 13, -w]$ $-e^{3} + 8e$
19 $[19, 19, -w^{2} - w + 4]$ $-\frac{1}{2}e^{5} + \frac{13}{2}e^{3} - \frac{37}{2}e$
23 $[23, 23, w^{2} + w - 10]$ $-3$
29 $[29, 29, 2w^{2} - 21]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{15}{2}e^{3} + \frac{47}{2}e$
37 $[37, 37, 2w^{2} + w - 17]$ $-e^{3} + 8e$
43 $[43, 43, 3w^{2} + 3w - 22]$ $\phantom{-}e^{3} - 6e$
47 $[47, 47, w^{2} - 6]$ $-e^{3} + 7e$
47 $[47, 47, w^{2} - 3]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{13}{2}e^{3} + \frac{33}{2}e$
47 $[47, 47, -w^{2} + 12]$ $-6$
53 $[53, 53, w^{2} - w - 4]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{13}{2}e^{3} + \frac{33}{2}e$
61 $[61, 61, w^{2} - 5]$ $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - \frac{23}{2}e$
67 $[67, 67, w^{2} - w - 7]$ $-\frac{1}{2}e^{5} + \frac{13}{2}e^{3} - \frac{31}{2}e$
73 $[73, 73, 7w^{2} + 3w - 66]$ $\phantom{-}2$
79 $[79, 79, 2w^{2} - 19]$ $-\frac{1}{2}e^{5} + \frac{13}{2}e^{3} - \frac{37}{2}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$8$ $[8, 2, 2]$ $-1$