Properties

Label 6.6.1541581.1-53.1-f
Base field 6.6.1541581.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $53$
Level $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$
Dimension $32$
CM no
Base change no

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Base field 6.6.1541581.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$
Dimension: $32$
CM: no
Base change: no
Newspace dimension: $56$

Hecke eigenvalues ($q$-expansion)

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

\(x^{32} - 19x^{31} + 71x^{30} + 856x^{29} - 7418x^{28} - 4016x^{27} + 225112x^{26} - 487113x^{25} - 3170177x^{24} + 13804884x^{23} + 17761909x^{22} - 179456426x^{21} + 80149177x^{20} + 1320803198x^{19} - 1990696844x^{18} - 5587935585x^{17} + 14596831425x^{16} + 11647688829x^{15} - 59427041680x^{14} + 2196458264x^{13} + 148450529193x^{12} - 76945495313x^{11} - 230388175743x^{10} + 201085243732x^{9} + 212600260175x^{8} - 262317019635x^{7} - 99939378620x^{6} + 188138745534x^{5} + 8367972022x^{4} - 69494248798x^{3} + 10371139384x^{2} + 10164696048x - 2777057104\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ $\phantom{-}e$
11 $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ $...$
11 $[11, 11, w^{2} - w - 2]$ $...$
17 $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ $...$
27 $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ $...$
27 $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $...$
37 $[37, 37, -w^{2} + 2w + 2]$ $...$
47 $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ $...$
53 $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ $-1$
59 $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ $...$
64 $[64, 2, -2]$ $...$
67 $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ $...$
67 $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ $...$
71 $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $...$
71 $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ $...$
73 $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ $...$
83 $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ $...$
83 $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ $...$
89 $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ $...$
97 $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$53$ $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ $1$