Properties

 Label 4.4.10025.1-19.1-e Base field 4.4.10025.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ Dimension $6$ CM no Base change no

Related objects

• L-function not available

Base field 4.4.10025.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 11x^{2} + 10x + 20$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} + 4x^{5} - 8x^{4} - 50x^{3} - 48x^{2} + 16x + 17$$
Norm Prime Eigenvalue
4 $[4, 2, -w + 2]$ $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{2}e^{4} - \frac{11}{4}e^{3} - \frac{25}{4}e^{2} - 2e + \frac{1}{4}$
4 $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ $-\frac{1}{4}e^{5} - \frac{1}{2}e^{4} + \frac{13}{4}e^{3} + \frac{25}{4}e^{2} - 3e - \frac{7}{4}$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ $-\frac{1}{2}e^{5} - e^{4} + \frac{11}{2}e^{3} + \frac{27}{2}e^{2} + 3e - \frac{9}{2}$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ $-1$
19 $[19, 19, w - 1]$ $-\frac{3}{4}e^{5} - e^{4} + \frac{37}{4}e^{3} + \frac{55}{4}e^{2} - \frac{15}{2}e - \frac{7}{4}$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 6e^{2} + \frac{15}{2}e - \frac{5}{2}$
31 $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ $-\frac{1}{2}e^{5} - e^{4} + \frac{13}{2}e^{3} + \frac{27}{2}e^{2} - 6e - \frac{17}{2}$
49 $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ $-\frac{7}{4}e^{5} - \frac{17}{4}e^{4} + 20e^{3} + \frac{217}{4}e^{2} + \frac{25}{4}e - \frac{43}{2}$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ $-e^{5} - \frac{9}{4}e^{4} + \frac{47}{4}e^{3} + \frac{57}{2}e^{2} + \frac{3}{4}e - \frac{43}{4}$
59 $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ $-\frac{5}{4}e^{5} - 3e^{4} + \frac{55}{4}e^{3} + \frac{157}{4}e^{2} + \frac{17}{2}e - \frac{45}{4}$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ $\phantom{-}\frac{3}{2}e^{5} + \frac{7}{2}e^{4} - 17e^{3} - \frac{91}{2}e^{2} - \frac{15}{2}e + 13$
61 $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ $\phantom{-}\frac{5}{4}e^{5} + \frac{7}{4}e^{4} - 15e^{3} - \frac{103}{4}e^{2} + \frac{33}{4}e + \frac{29}{2}$
61 $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{2}e^{4} - \frac{9}{4}e^{3} - \frac{25}{4}e^{2} - 6e + \frac{15}{4}$
71 $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ $-\frac{1}{4}e^{5} - \frac{3}{4}e^{4} + 2e^{3} + \frac{39}{4}e^{2} + \frac{43}{4}e - \frac{1}{2}$
71 $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ $-\frac{1}{2}e^{5} - \frac{3}{2}e^{4} + 5e^{3} + \frac{37}{2}e^{2} + \frac{21}{2}e + 2$
79 $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ $-e^{5} - e^{4} + 12e^{3} + 15e^{2} - 11e - 2$
79 $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ $-\frac{1}{2}e^{5} - \frac{7}{4}e^{4} + \frac{23}{4}e^{3} + 20e^{2} + \frac{13}{4}e + \frac{1}{4}$
81 $[81, 3, -3]$ $\phantom{-}\frac{3}{4}e^{5} + \frac{7}{4}e^{4} - \frac{17}{2}e^{3} - \frac{93}{4}e^{2} - \frac{3}{4}e + 9$
89 $[89, 89, w^{3} - 7w + 1]$ $\phantom{-}\frac{5}{4}e^{5} + \frac{13}{4}e^{4} - \frac{29}{2}e^{3} - \frac{159}{4}e^{2} - \frac{13}{4}e + 12$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ $1$