# Properties

 Base field 6.6.434581.1 Weight [2, 2, 2, 2, 2, 2] Level norm 71 Level $[71,71,w^{5} - 3w^{4} - 2w^{3} + 7w^{2} + w]$ Label 6.6.434581.1-71.3-d Dimension 5 CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.434581.1

Generator $$w$$, with minimal polynomial $$x^{6} - 2x^{5} - 4x^{4} + 5x^{3} + 4x^{2} - 2x - 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2, 2, 2] Level $[71,71,w^{5} - 3w^{4} - 2w^{3} + 7w^{2} + w]$ Label 6.6.434581.1-71.3-d Dimension 5 Is CM no Is base change no Parent newspace dimension 9

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5}$$ $$\mathstrut -\mathstrut 3x^{4}$$ $$\mathstrut -\mathstrut 41x^{3}$$ $$\mathstrut +\mathstrut 35x^{2}$$ $$\mathstrut +\mathstrut 448x$$ $$\mathstrut +\mathstrut 506$$
Norm Prime Eigenvalue
13 $[13, 13, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + w + 4]$ $-\frac{25}{161}e^{4} + \frac{5}{7}e^{3} + \frac{841}{161}e^{2} - \frac{2285}{161}e - \frac{300}{7}$
13 $[13, 13, -w^{2} + w + 2]$ $\phantom{-}e$
27 $[27, 3, 2w^{5} - 4w^{4} - 7w^{3} + 9w^{2} + 4w - 2]$ $-\frac{45}{161}e^{4} + \frac{9}{7}e^{3} + \frac{1385}{161}e^{2} - \frac{3791}{161}e - \frac{470}{7}$
27 $[27, 3, -2w^{5} + 5w^{4} + 5w^{3} - 12w^{2} - w + 5]$ $\phantom{-}\frac{40}{161}e^{4} - \frac{8}{7}e^{3} - \frac{1249}{161}e^{2} + \frac{3334}{161}e + \frac{438}{7}$
29 $[29, 29, w^{3} - 2w^{2} - 2w + 3]$ $\phantom{-}\frac{53}{161}e^{4} - \frac{12}{7}e^{3} - \frac{1667}{161}e^{2} + \frac{5456}{161}e + \frac{650}{7}$
29 $[29, 29, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 4w - 2]$ $-\frac{68}{161}e^{4} + \frac{15}{7}e^{3} + \frac{2075}{161}e^{2} - \frac{6505}{161}e - \frac{739}{7}$
43 $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$ $-\frac{50}{161}e^{4} + \frac{10}{7}e^{3} + \frac{1682}{161}e^{2} - \frac{4570}{161}e - \frac{593}{7}$
43 $[43, 43, -w^{4} + w^{3} + 5w^{2} - 4]$ $-\frac{13}{161}e^{4} + \frac{4}{7}e^{3} + \frac{418}{161}e^{2} - \frac{2122}{161}e - \frac{191}{7}$
49 $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$ $\phantom{-}\frac{9}{23}e^{4} - 2e^{3} - \frac{277}{23}e^{2} + \frac{887}{23}e + 98$
64 $[64, 2, -2]$ $-\frac{4}{23}e^{4} + e^{3} + \frac{118}{23}e^{2} - \frac{453}{23}e - 45$
71 $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ $\phantom{-}\frac{18}{161}e^{4} - \frac{5}{7}e^{3} - \frac{393}{161}e^{2} + \frac{1935}{161}e + \frac{97}{7}$
71 $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ $\phantom{-}\frac{45}{161}e^{4} - \frac{9}{7}e^{3} - \frac{1385}{161}e^{2} + \frac{3791}{161}e + \frac{442}{7}$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ $-1$
71 $[71, 71, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 3w + 5]$ $\phantom{-}\frac{10}{161}e^{4} - \frac{2}{7}e^{3} - \frac{272}{161}e^{2} + \frac{592}{161}e + \frac{92}{7}$
83 $[83, 83, -3w^{5} + 7w^{4} + 9w^{3} - 17w^{2} - 5w + 5]$ $\phantom{-}\frac{15}{161}e^{4} - \frac{3}{7}e^{3} - \frac{569}{161}e^{2} + \frac{1693}{161}e + \frac{215}{7}$
83 $[83, 83, 3w^{5} - 6w^{4} - 10w^{3} + 12w^{2} + 5w - 2]$ $-\frac{15}{161}e^{4} + \frac{3}{7}e^{3} + \frac{569}{161}e^{2} - \frac{1371}{161}e - \frac{222}{7}$
83 $[83, 83, -2w^{5} + 5w^{4} + 5w^{3} - 11w^{2} - 3w + 3]$ $\phantom{-}\frac{93}{161}e^{4} - \frac{20}{7}e^{3} - \frac{2916}{161}e^{2} + \frac{8951}{161}e + \frac{1095}{7}$
83 $[83, 83, 3w^{5} - 7w^{4} - 8w^{3} + 15w^{2} + 2w - 4]$ $\phantom{-}\frac{38}{161}e^{4} - \frac{9}{7}e^{3} - \frac{1098}{161}e^{2} + \frac{3763}{161}e + \frac{428}{7}$
97 $[97, 97, -3w^{5} + 6w^{4} + 10w^{3} - 12w^{2} - 5w + 3]$ $\phantom{-}\frac{30}{161}e^{4} - \frac{6}{7}e^{3} - \frac{1138}{161}e^{2} + \frac{3064}{161}e + \frac{486}{7}$
97 $[97, 97, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 3]$ $\phantom{-}\frac{12}{161}e^{4} - \frac{1}{7}e^{3} - \frac{584}{161}e^{2} + \frac{807}{161}e + \frac{249}{7}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
71 $[71,71,w^{5} - 3w^{4} - 2w^{3} + 7w^{2} + w]$ $1$