Properties

Label 4.4.16225.1-19.2-b
Base field 4.4.16225.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19,19,\frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$
Dimension $17$
CM no
Base change no

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Base field 4.4.16225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 6x + 36\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[19,19,\frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$
Dimension: $17$
CM: no
Base change: no
Newspace dimension: $34$

Hecke eigenvalues ($q$-expansion)

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

\(x^{17} + 7x^{16} - 20x^{15} - 227x^{14} - 30x^{13} + 2606x^{12} + 2633x^{11} - 13425x^{10} - 17160x^{9} + 34091x^{8} + 36066x^{7} - 53023x^{6} - 22398x^{5} + 42360x^{4} - 8562x^{3} - 4202x^{2} + 1422x - 107\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ $...$
4 $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ $...$
9 $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ $...$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ $...$
19 $[19, 19, w + 1]$ $...$
19 $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ $\phantom{-}1$
25 $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ $...$
29 $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ $...$
29 $[29, 29, w - 1]$ $...$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ $...$
31 $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ $...$
41 $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ $...$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ $...$
59 $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $...$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ $...$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ $...$
79 $[79, 79, w^{2} - 11]$ $...$
79 $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ $...$
89 $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,\frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ $-1$