# Properties

 Base field 5.5.160801.1 Weight [2, 2, 2, 2, 2] Level norm 27 Level $[27, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ Label 5.5.160801.1-27.1-d Dimension 7 CM no Base change no

# Related objects

• L-function not available

## Base field 5.5.160801.1

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

## Form

 Weight [2, 2, 2, 2, 2] Level $[27, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ Label 5.5.160801.1-27.1-d Dimension 7 Is CM no Is base change no Parent newspace dimension 25

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{7}$$ $$\mathstrut -\mathstrut 6x^{6}$$ $$\mathstrut -\mathstrut 28x^{5}$$ $$\mathstrut +\mathstrut 182x^{4}$$ $$\mathstrut +\mathstrut 40x^{3}$$ $$\mathstrut -\mathstrut 664x^{2}$$ $$\mathstrut +\mathstrut 288x$$ $$\mathstrut -\mathstrut 32$$
Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-1$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $\phantom{-}1$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}e$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}\frac{3}{32}e^{6} - \frac{9}{16}e^{5} - \frac{11}{4}e^{4} + \frac{273}{16}e^{3} + \frac{31}{4}e^{2} - 62e + \frac{27}{2}$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}\frac{3}{32}e^{6} - \frac{9}{16}e^{5} - \frac{11}{4}e^{4} + \frac{273}{16}e^{3} + \frac{31}{4}e^{2} - 62e + \frac{27}{2}$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{3}{16}e^{6} - \frac{17}{16}e^{5} - \frac{11}{2}e^{4} + \frac{257}{8}e^{3} + \frac{119}{8}e^{2} - \frac{461}{4}e + \frac{55}{2}$
23 $[23, 23, -w^{2} + 3]$ $-\frac{9}{32}e^{6} + \frac{13}{8}e^{5} + \frac{33}{4}e^{4} - \frac{787}{16}e^{3} - \frac{181}{8}e^{2} + \frac{709}{4}e - 39$
31 $[31, 31, w^{3} - 4w + 2]$ $-\frac{21}{32}e^{6} + \frac{61}{16}e^{5} + \frac{77}{4}e^{4} - \frac{1855}{16}e^{3} - 53e^{2} + \frac{859}{2}e - \frac{183}{2}$
32 $[32, 2, 2]$ $-\frac{29}{64}e^{6} + \frac{41}{16}e^{5} + \frac{107}{8}e^{4} - \frac{2487}{32}e^{3} - \frac{617}{16}e^{2} + \frac{2273}{8}e - \frac{117}{2}$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}\frac{27}{32}e^{6} - \frac{39}{8}e^{5} - \frac{99}{4}e^{4} + \frac{2369}{16}e^{3} + \frac{543}{8}e^{2} - \frac{2179}{4}e + 117$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $-\frac{3}{16}e^{6} + \frac{17}{16}e^{5} + \frac{11}{2}e^{4} - \frac{257}{8}e^{3} - \frac{119}{8}e^{2} + \frac{461}{4}e - \frac{51}{2}$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $\phantom{-}\frac{1}{32}e^{5} - \frac{5}{4}e^{3} + \frac{3}{16}e^{2} + \frac{75}{8}e - \frac{7}{4}$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $-\frac{1}{8}e^{6} + \frac{3}{4}e^{5} + \frac{7}{2}e^{4} - \frac{91}{4}e^{3} - 5e^{2} + 83e - 26$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $\phantom{-}\frac{1}{32}e^{6} - \frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{123}{16}e^{3} - \frac{17}{8}e^{2} - \frac{115}{4}e + 18$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-\frac{21}{32}e^{6} + \frac{61}{16}e^{5} + \frac{77}{4}e^{4} - \frac{1855}{16}e^{3} - 53e^{2} + \frac{857}{2}e - \frac{187}{2}$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $-\frac{11}{32}e^{6} + \frac{63}{32}e^{5} + \frac{41}{4}e^{4} - \frac{957}{16}e^{3} - \frac{517}{16}e^{2} + \frac{1767}{8}e - \frac{161}{4}$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $\phantom{-}\frac{1}{32}e^{6} - \frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{123}{16}e^{3} - \frac{17}{8}e^{2} - \frac{115}{4}e + 14$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $\phantom{-}\frac{7}{32}e^{6} - \frac{5}{4}e^{5} - \frac{25}{4}e^{4} + \frac{605}{16}e^{3} + \frac{105}{8}e^{2} - \frac{553}{4}e + 36$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $\phantom{-}\frac{33}{32}e^{6} - \frac{191}{32}e^{5} - \frac{121}{4}e^{4} + \frac{2903}{16}e^{3} + \frac{1321}{16}e^{2} - \frac{5371}{8}e + \frac{609}{4}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $\phantom{-}\frac{25}{32}e^{6} - \frac{73}{16}e^{5} - \frac{91}{4}e^{4} + \frac{2219}{16}e^{3} + 58e^{2} - \frac{1021}{2}e + \frac{239}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $1$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $-1$