Properties

Label 5.5.138136.1-29.1-a
Base field 5.5.138136.1
Weight $[2, 2, 2, 2, 2]$
Level norm $29$
Level $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$
Dimension $19$
CM no
Base change no

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Base field 5.5.138136.1

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

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$
Dimension: $19$
CM: no
Base change: no
Newspace dimension: $43$

Hecke eigenvalues ($q$-expansion)

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

\(x^{19} + 3x^{18} - 23x^{17} - 71x^{16} + 214x^{15} + 687x^{14} - 1037x^{13} - 3510x^{12} + 2823x^{11} + 10223x^{10} - 4413x^{9} - 17168x^{8} + 4009x^{7} + 16113x^{6} - 2071x^{5} - 7672x^{4} + 504x^{3} + 1439x^{2} - 32x - 15\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
7 $[7, 7, -2w^{4} + w^{3} + 12w^{2} + w - 5]$ $...$
8 $[8, 2, w^{4} - 7w^{2} - 3w + 5]$ $...$
19 $[19, 19, -2w^{4} + w^{3} + 12w^{2} - 5]$ $...$
19 $[19, 19, -w^{3} + w^{2} + 5w - 1]$ $...$
29 $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ $-1$
31 $[31, 31, -2w^{4} + w^{3} + 12w^{2} + 2w - 5]$ $...$
37 $[37, 37, -2w^{4} + 13w^{2} + 5w - 7]$ $...$
53 $[53, 53, 3w^{4} - 2w^{3} - 18w^{2} + 3w + 9]$ $...$
59 $[59, 59, 2w^{4} - 13w^{2} - 6w + 5]$ $...$
61 $[61, 61, -3w^{4} + 2w^{3} + 18w^{2} - 2w - 11]$ $...$
61 $[61, 61, w^{2} - w - 3]$ $...$
61 $[61, 61, 6w^{4} - 2w^{3} - 38w^{2} - 6w + 23]$ $...$
67 $[67, 67, -w^{4} + 7w^{2} + 4w - 5]$ $...$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 1]$ $...$
71 $[71, 71, -w^{2} + 3]$ $...$
73 $[73, 73, 3w^{4} - w^{3} - 19w^{2} - 3w + 9]$ $...$
79 $[79, 79, 3w^{4} - w^{3} - 19w^{2} - 4w + 11]$ $...$
83 $[83, 83, -w^{4} - w^{3} + 7w^{2} + 8w - 3]$ $...$
97 $[97, 97, -2w^{4} + w^{3} + 12w^{2} + 2w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ $1$