# Properties

 Label 4.4.17069.1-17.3-e Base field 4.4.17069.1 Weight $[2, 2, 2, 2]$ Level norm $17$ Level $[17,17,w^{3} - 3w^{2} - 2w + 2]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.17069.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[17,17,w^{3} - 3w^{2} - 2w + 2]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $37$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 13x^{4} - 2x^{3} + 40x^{2} + 21x - 8$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ $\phantom{-}\frac{4}{19}e^{5} + \frac{3}{19}e^{4} - \frac{45}{19}e^{3} - \frac{18}{19}e^{2} + \frac{99}{19}e + \frac{11}{19}$
9 $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $\phantom{-}\frac{2}{19}e^{5} - \frac{8}{19}e^{4} - \frac{32}{19}e^{3} + \frac{67}{19}e^{2} + \frac{97}{19}e - \frac{23}{19}$
16 $[16, 2, 2]$ $-\frac{5}{19}e^{5} + \frac{1}{19}e^{4} + \frac{61}{19}e^{3} - \frac{25}{19}e^{2} - \frac{157}{19}e + \frac{29}{19}$
17 $[17, 17, w^{3} - w^{2} - 8w - 5]$ $-\frac{6}{19}e^{5} + \frac{5}{19}e^{4} + \frac{58}{19}e^{3} - \frac{68}{19}e^{2} - \frac{82}{19}e + \frac{69}{19}$
17 $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ $\phantom{-}\frac{2}{19}e^{5} - \frac{8}{19}e^{4} - \frac{32}{19}e^{3} + \frac{67}{19}e^{2} + \frac{97}{19}e - \frac{61}{19}$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}1$
17 $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ $-\frac{2}{19}e^{5} + \frac{8}{19}e^{4} + \frac{32}{19}e^{3} - \frac{67}{19}e^{2} - \frac{97}{19}e - \frac{15}{19}$
25 $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ $-\frac{12}{19}e^{5} - \frac{9}{19}e^{4} + \frac{116}{19}e^{3} + \frac{54}{19}e^{2} - \frac{183}{19}e + \frac{5}{19}$
25 $[25, 5, w^{2} - 2w - 7]$ $\phantom{-}\frac{2}{19}e^{5} + \frac{11}{19}e^{4} - \frac{13}{19}e^{3} - \frac{85}{19}e^{2} - \frac{17}{19}e + \frac{34}{19}$
29 $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ $-\frac{6}{19}e^{5} + \frac{5}{19}e^{4} + \frac{77}{19}e^{3} - \frac{30}{19}e^{2} - \frac{196}{19}e - \frac{45}{19}$
29 $[29, 29, w - 2]$ $\phantom{-}\frac{5}{19}e^{5} - \frac{1}{19}e^{4} - \frac{23}{19}e^{3} + \frac{25}{19}e^{2} - \frac{90}{19}e - \frac{86}{19}$
53 $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ $\phantom{-}\frac{10}{19}e^{5} - \frac{2}{19}e^{4} - \frac{122}{19}e^{3} - \frac{7}{19}e^{2} + \frac{333}{19}e + \frac{189}{19}$
53 $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ $-\frac{5}{19}e^{5} + \frac{1}{19}e^{4} + \frac{42}{19}e^{3} - \frac{6}{19}e^{2} - \frac{5}{19}e - \frac{104}{19}$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ $\phantom{-}\frac{6}{19}e^{5} + \frac{14}{19}e^{4} - \frac{58}{19}e^{3} - \frac{103}{19}e^{2} + \frac{101}{19}e - \frac{12}{19}$
61 $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ $-\frac{10}{19}e^{5} + \frac{40}{19}e^{4} + \frac{141}{19}e^{3} - \frac{335}{19}e^{2} - \frac{447}{19}e + \frac{210}{19}$
101 $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ $\phantom{-}\frac{4}{19}e^{5} + \frac{3}{19}e^{4} - \frac{7}{19}e^{3} + \frac{58}{19}e^{2} - \frac{186}{19}e - \frac{274}{19}$
103 $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}\frac{2}{19}e^{5} + \frac{11}{19}e^{4} + \frac{6}{19}e^{3} - \frac{123}{19}e^{2} - \frac{131}{19}e + \frac{262}{19}$
103 $[103, 103, -w^{3} + w^{2} + 8w + 2]$ $-\frac{2}{19}e^{5} + \frac{27}{19}e^{4} + \frac{51}{19}e^{3} - \frac{200}{19}e^{2} - \frac{211}{19}e + \frac{4}{19}$
113 $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}\frac{13}{19}e^{5} - \frac{14}{19}e^{4} - \frac{132}{19}e^{3} + \frac{84}{19}e^{2} + \frac{184}{19}e - \frac{7}{19}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17,17,w^{3} - 3w^{2} - 2w + 2]$ $-1$