Properties

Label 3.3.1937.1-19.1-c
Base field 3.3.1937.1
Weight $[2, 2, 2]$
Level norm $19$
Level $[19, 19, -w^{2} + 2w + 4]$
Dimension $31$
CM no
Base change no

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Base field 3.3.1937.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[19, 19, -w^{2} + 2w + 4]$
Dimension: $31$
CM: no
Base change: no
Newspace dimension: $64$

Hecke eigenvalues ($q$-expansion)

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

\(x^{31} - 6x^{30} - 41x^{29} + 293x^{28} + 687x^{27} - 6321x^{26} - 5835x^{25} + 79726x^{24} + 22615x^{23} - 655236x^{22} + 18208x^{21} + 3698066x^{20} - 598155x^{19} - 14692150x^{18} + 2714593x^{17} + 41337624x^{16} - 5606986x^{15} - 81497072x^{14} + 3628191x^{13} + 109443769x^{12} + 6656685x^{11} - 95471494x^{10} - 14850682x^{9} + 50665818x^{8} + 11319528x^{7} - 14970223x^{6} - 3829211x^{5} + 2165635x^{4} + 526733x^{3} - 121378x^{2} - 16677x + 2714\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w - 2]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $...$
7 $[7, 7, w - 3]$ $...$
8 $[8, 2, 2]$ $...$
9 $[9, 3, w^{2} - 3w - 2]$ $...$
13 $[13, 13, w + 3]$ $...$
13 $[13, 13, -w + 2]$ $...$
19 $[19, 19, -w^{2} + 2w + 4]$ $\phantom{-}1$
23 $[23, 23, w^{2} - 4w + 1]$ $...$
25 $[25, 5, w^{2} - 2w - 1]$ $...$
31 $[31, 31, w^{2} - 2w - 9]$ $...$
37 $[37, 37, -w^{2} + 3w + 3]$ $...$
41 $[41, 41, w^{2} - w - 1]$ $...$
41 $[41, 41, w^{2} - w - 5]$ $...$
41 $[41, 41, w^{2} - w - 10]$ $...$
43 $[43, 43, -2w - 3]$ $...$
47 $[47, 47, -w^{2} - w + 4]$ $...$
49 $[49, 7, -w^{2} + 5w - 5]$ $...$
59 $[59, 59, w^{2} - w - 4]$ $...$
59 $[59, 59, w^{2} - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, -w^{2} + 2w + 4]$ $-1$