Properties

Base field 4.4.16997.1
Weight [2, 2, 2, 2]
Level norm 19
Level $[19, 19, -w^{2} + w + 1]$
Label 4.4.16997.1-19.1-b
Dimension 19
CM no
Base change no

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Base field 4.4.16997.1

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

Form

Weight [2, 2, 2, 2]
Level $[19, 19, -w^{2} + w + 1]$
Label 4.4.16997.1-19.1-b
Dimension 19
Is CM no
Is base change no
Parent newspace dimension 34

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{19} - 9x^{18} - 17x^{17} + 378x^{16} - 555x^{15} - 5272x^{14} + 16210x^{13} + 23739x^{12} - 140998x^{11} + 37716x^{10} + 474183x^{9} - 423432x^{8} - 679873x^{7} + 794612x^{6} + 497875x^{5} - 568613x^{4} - 212944x^{3} + 142776x^{2} + 30032x - 11984\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w]$ $...$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2]$ $...$
13 $[13, 13, -w^{2} + 3]$ $...$
13 $[13, 13, w^{2} - w - 4]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, -w^{2} + w + 1]$ $-1$
23 $[23, 23, -w^{3} + 4w + 2]$ $...$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $...$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $...$
29 $[29, 29, -w + 3]$ $...$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $...$
37 $[37, 37, w^{3} - 4w - 1]$ $...$
37 $[37, 37, w^{3} - 3w + 1]$ $...$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $...$
59 $[59, 59, w^{2} + w - 4]$ $...$
61 $[61, 61, -2w^{2} + w + 8]$ $...$
73 $[73, 73, -w^{3} + 5w - 1]$ $...$
79 $[79, 79, 2w^{2} + w - 6]$ $...$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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