Properties

Label 6.6.1683101.1-41.2-b
Base field 6.6.1683101.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $41$
Level $[41,41,-w^{2} + 2w + 3]$
Dimension $19$
CM no
Base change no

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Base field 6.6.1683101.1

Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[41,41,-w^{2} + 2w + 3]$
Dimension: $19$
CM: no
Base change: no
Newspace dimension: $45$

Hecke eigenvalues ($q$-expansion)

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

\(x^{19} + 12x^{18} + 12x^{17} - 388x^{16} - 1529x^{15} + 2428x^{14} + 22725x^{13} + 19988x^{12} - 104268x^{11} - 217512x^{10} + 62284x^{9} + 490233x^{8} + 369858x^{7} - 3940x^{6} - 62299x^{5} + 2106x^{4} + 4131x^{3} - 784x^{2} + 51x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w]$ $...$
7 $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ $\phantom{-}e$
13 $[13, 13, w^{2} - 3]$ $...$
13 $[13, 13, -w^{2} + 2w + 2]$ $...$
29 $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ $...$
29 $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ $...$
41 $[41, 41, -w^{2} + 4]$ $...$
41 $[41, 41, -w^{2} + 2w + 3]$ $\phantom{-}1$
43 $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ $...$
43 $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ $...$
64 $[64, 2, -2]$ $...$
71 $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ $...$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ $...$
71 $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ $...$
71 $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ $...$
83 $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ $...$
83 $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ $...$
97 $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ $...$
97 $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ $...$
113 $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41,41,-w^{2} + 2w + 3]$ $-1$