Properties

Label 5.5.138136.1-19.2-e
Base field 5.5.138136.1
Weight $[2, 2, 2, 2, 2]$
Level norm $19$
Level $[19, 19, -w^{3} + w^{2} + 5w - 1]$
Dimension $16$
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: $[19, 19, -w^{3} + w^{2} + 5w - 1]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $29$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} - 4x^{15} - 22x^{14} + 101x^{13} + 177x^{12} - 1035x^{11} - 551x^{10} + 5544x^{9} - 306x^{8} - 16618x^{7} + 6443x^{6} + 27546x^{5} - 16204x^{4} - 23056x^{3} + 16288x^{2} + 7488x - 5760\)

  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 $[19, 19, -w^{3} + w^{2} + 5w - 1]$ $\phantom{-}1$
29 $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ $...$
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 $[67, 67, -w^{4} + 7w^{2} + 4w - 5]$ $-\frac{103}{4}e^{15} + \frac{257}{4}e^{14} + 663e^{13} - \frac{6409}{4}e^{12} - \frac{13931}{2}e^{11} + 16152e^{10} + 38475e^{9} - \frac{338849}{4}e^{8} - 119583e^{7} + 247347e^{6} + \frac{826133}{4}e^{5} - \frac{1588831}{4}e^{4} - 181276e^{3} + 319580e^{2} + 62478e - 98284$
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
$19$ $[19, 19, -w^{3} + w^{2} + 5w - 1]$ $-1$