# Properties

 Label 4.4.13025.1-19.1-c Base field 4.4.13025.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ Dimension $8$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13025.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 12x^{2} + 3x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ Dimension: $8$ CM: no Base change: no Newspace dimension: $23$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{8} + 2x^{7} - 14x^{6} - 22x^{5} + 53x^{4} + 66x^{3} - 44x^{2} - 40x - 5$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ $-\frac{1}{8}e^{7} - \frac{1}{8}e^{6} + 2e^{5} + \frac{9}{8}e^{4} - 9e^{3} - \frac{23}{8}e^{2} + \frac{81}{8}e + \frac{5}{4}$
4 $[4, 2, -w^{2} + w + 8]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + \frac{3}{2}$
5 $[5, 5, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{9}{2}]$ $\phantom{-}\frac{1}{4}e^{7} + \frac{3}{8}e^{6} - \frac{29}{8}e^{5} - \frac{15}{4}e^{4} + \frac{115}{8}e^{3} + \frac{43}{4}e^{2} - \frac{115}{8}e - \frac{53}{8}$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ $\phantom{-}1$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{41}{4}]$ $-\frac{1}{8}e^{7} - \frac{1}{4}e^{6} + \frac{15}{8}e^{5} + \frac{25}{8}e^{4} - \frac{61}{8}e^{3} - \frac{87}{8}e^{2} + 5e + \frac{55}{8}$
29 $[29, 29, w]$ $\phantom{-}\frac{3}{8}e^{7} + \frac{5}{8}e^{6} - \frac{23}{4}e^{5} - \frac{53}{8}e^{4} + \frac{103}{4}e^{3} + \frac{143}{8}e^{2} - \frac{253}{8}e - \frac{25}{4}$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{1}{2}w + \frac{1}{4}]$ $\phantom{-}\frac{1}{4}e^{7} + \frac{3}{8}e^{6} - \frac{27}{8}e^{5} - \frac{13}{4}e^{4} + \frac{89}{8}e^{3} + \frac{25}{4}e^{2} - \frac{33}{8}e - \frac{5}{8}$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{9}{4}]$ $\phantom{-}\frac{1}{8}e^{6} - \frac{1}{8}e^{5} - \frac{5}{2}e^{4} + \frac{11}{8}e^{3} + \frac{23}{2}e^{2} - \frac{17}{8}e - \frac{65}{8}$
29 $[29, 29, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{5}{2}]$ $-\frac{1}{8}e^{6} - \frac{3}{8}e^{5} + \frac{7}{4}e^{4} + \frac{33}{8}e^{3} - \frac{27}{4}e^{2} - \frac{71}{8}e + \frac{15}{8}$
41 $[41, 41, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{47}{4}]$ $-\frac{5}{8}e^{7} - e^{6} + \frac{73}{8}e^{5} + \frac{85}{8}e^{4} - \frac{287}{8}e^{3} - \frac{247}{8}e^{2} + \frac{129}{4}e + \frac{89}{8}$
41 $[41, 41, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{15}{4}]$ $-\frac{1}{2}e^{7} - \frac{7}{8}e^{6} + \frac{55}{8}e^{5} + \frac{17}{2}e^{4} - \frac{209}{8}e^{3} - 22e^{2} + \frac{215}{8}e + \frac{79}{8}$
61 $[61, 61, -\frac{3}{2}w^{3} + 3w^{2} + 11w - \frac{21}{2}]$ $-\frac{1}{2}e^{7} - \frac{7}{8}e^{6} + \frac{57}{8}e^{5} + \frac{35}{4}e^{4} - \frac{219}{8}e^{3} - \frac{83}{4}e^{2} + \frac{193}{8}e + \frac{29}{8}$
61 $[61, 61, w^{3} - 2w^{2} - 4w + 6]$ $-\frac{3}{4}e^{7} - e^{6} + \frac{23}{2}e^{5} + \frac{41}{4}e^{4} - \frac{99}{2}e^{3} - \frac{121}{4}e^{2} + \frac{223}{4}e + \frac{67}{4}$
79 $[79, 79, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{27}{4}]$ $-\frac{9}{8}e^{7} - 2e^{6} + \frac{125}{8}e^{5} + \frac{155}{8}e^{4} - \frac{471}{8}e^{3} - \frac{373}{8}e^{2} + \frac{207}{4}e + \frac{135}{8}$
79 $[79, 79, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{35}{4}]$ $-\frac{1}{4}e^{7} - \frac{1}{8}e^{6} + \frac{29}{8}e^{5} - \frac{1}{4}e^{4} - \frac{107}{8}e^{3} + \frac{15}{4}e^{2} + \frac{103}{8}e + \frac{15}{8}$
81 $[81, 3, -3]$ $-\frac{1}{2}e^{7} - \frac{1}{2}e^{6} + \frac{15}{2}e^{5} + \frac{15}{4}e^{4} - \frac{59}{2}e^{3} - \frac{17}{4}e^{2} + 26e - \frac{23}{4}$
89 $[89, 89, \frac{7}{4}w^{3} - \frac{11}{2}w^{2} - \frac{21}{2}w + \frac{119}{4}]$ $\phantom{-}\frac{1}{2}e^{7} + \frac{9}{8}e^{6} - \frac{61}{8}e^{5} - \frac{27}{2}e^{4} + \frac{275}{8}e^{3} + \frac{81}{2}e^{2} - \frac{337}{8}e - \frac{125}{8}$
89 $[89, 89, \frac{1}{4}w^{3} + \frac{3}{2}w^{2} - \frac{3}{2}w - \frac{23}{4}]$ $\phantom{-}\frac{3}{4}e^{7} + \frac{7}{4}e^{6} - 10e^{5} - \frac{75}{4}e^{4} + \frac{73}{2}e^{3} + \frac{203}{4}e^{2} - \frac{109}{4}e - \frac{45}{2}$
109 $[109, 109, -\frac{1}{2}w^{3} + 3w^{2} + 2w - \frac{41}{2}]$ $-\frac{9}{8}e^{7} - \frac{9}{4}e^{6} + \frac{121}{8}e^{5} + \frac{181}{8}e^{4} - \frac{439}{8}e^{3} - \frac{459}{8}e^{2} + \frac{189}{4}e + \frac{135}{8}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ $-1$