# Properties

 Label 4.4.13525.1-16.1-b Base field 4.4.13525.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13525.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 12x^{2} + 8x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $21$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} + x^{5} - 15x^{4} + 61x^{2} - 57x + 13$$
Norm Prime Eigenvalue
5 $[5, 5, -w + 2]$ $\phantom{-}e$
5 $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $-\frac{1}{2}e^{5} - e^{4} + \frac{13}{2}e^{3} + \frac{11}{2}e^{2} - 26e + \frac{21}{2}$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + 4e^{2} + \frac{17}{2}e - \frac{17}{2}$
9 $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - 4e^{2} - \frac{17}{2}e + \frac{17}{2}$
11 $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ $-\frac{1}{4}e^{5} + \frac{17}{4}e^{3} - \frac{3}{4}e^{2} - \frac{35}{2}e + \frac{29}{4}$
11 $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ $\phantom{-}\frac{3}{4}e^{5} + e^{4} - \frac{43}{4}e^{3} - \frac{19}{4}e^{2} + \frac{85}{2}e - \frac{79}{4}$
16 $[16, 2, 2]$ $\phantom{-}1$
29 $[29, 29, -w]$ $-\frac{3}{4}e^{5} - \frac{3}{2}e^{4} + \frac{37}{4}e^{3} + \frac{31}{4}e^{2} - 35e + \frac{65}{4}$
29 $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ $-\frac{1}{4}e^{5} - \frac{1}{2}e^{4} + \frac{11}{4}e^{3} + \frac{9}{4}e^{2} - 8e + \frac{23}{4}$
41 $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ $-\frac{1}{4}e^{5} + \frac{1}{2}e^{4} + \frac{27}{4}e^{3} - \frac{11}{4}e^{2} - 30e + \frac{43}{4}$
41 $[41, 41, -w^{2} + 10]$ $\phantom{-}\frac{7}{4}e^{5} + 3e^{4} - \frac{91}{4}e^{3} - \frac{67}{4}e^{2} + \frac{165}{2}e - \frac{131}{4}$
41 $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ $\phantom{-}\frac{1}{4}e^{5} + e^{4} - \frac{13}{4}e^{3} - \frac{21}{4}e^{2} + \frac{35}{2}e - \frac{69}{4}$
41 $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{2}e^{4} - \frac{15}{4}e^{3} + \frac{23}{4}e^{2} + 9e - \frac{47}{4}$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ $\phantom{-}\frac{1}{2}e^{5} + e^{4} - \frac{17}{2}e^{3} - \frac{13}{2}e^{2} + 41e - \frac{39}{2}$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ $\phantom{-}\frac{1}{2}e^{5} + e^{4} - \frac{15}{2}e^{3} - \frac{15}{2}e^{2} + 30e - \frac{17}{2}$
59 $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ $-\frac{1}{4}e^{5} + \frac{17}{4}e^{3} - \frac{7}{4}e^{2} - \frac{35}{2}e + \frac{65}{4}$
59 $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ $-\frac{1}{4}e^{5} - e^{4} + \frac{5}{4}e^{3} + \frac{25}{4}e^{2} - \frac{1}{2}e - \frac{3}{4}$
61 $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ $\phantom{-}\frac{5}{4}e^{5} + 2e^{4} - \frac{65}{4}e^{3} - \frac{37}{4}e^{2} + \frac{119}{2}e - \frac{133}{4}$
61 $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ $\phantom{-}\frac{3}{4}e^{5} + 2e^{4} - \frac{31}{4}e^{3} - \frac{43}{4}e^{2} + \frac{53}{2}e - \frac{67}{4}$
71 $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ $\phantom{-}\frac{3}{4}e^{5} + e^{4} - \frac{47}{4}e^{3} - \frac{15}{4}e^{2} + \frac{105}{2}e - \frac{135}{4}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $-1$