# Properties

 Base field 4.4.15952.1 Weight [2, 2, 2, 2] Level norm 11 Level $[11, 11, -w + 2]$ Label 4.4.15952.1-11.2-g Dimension 10 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.15952.1

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

## Form

 Weight [2, 2, 2, 2] Level $[11, 11, -w + 2]$ Label 4.4.15952.1-11.2-g Dimension 10 Is CM no Is base change no Parent newspace dimension 22

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{10}$$ $$\mathstrut -\mathstrut 16x^{8}$$ $$\mathstrut +\mathstrut 90x^{6}$$ $$\mathstrut -\mathstrut 218x^{4}$$ $$\mathstrut +\mathstrut 215x^{2}$$ $$\mathstrut -\mathstrut 64$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}\frac{1}{4}e^{9} - \frac{7}{2}e^{7} + 16e^{5} - 28e^{3} + \frac{57}{4}e$
11 $[11, 11, -w^{3} + 5w + 1]$ $\phantom{-}\frac{1}{2}e^{9} - \frac{13}{2}e^{7} + \frac{53}{2}e^{5} - \frac{83}{2}e^{3} + 24e$
11 $[11, 11, -w + 2]$ $-1$
13 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $-\frac{1}{2}e^{9} + \frac{13}{2}e^{7} - \frac{51}{2}e^{5} + \frac{65}{2}e^{3} - 7e$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $-\frac{1}{4}e^{9} + 4e^{7} - \frac{43}{2}e^{5} + \frac{87}{2}e^{3} - \frac{95}{4}e$
17 $[17, 17, -w^{2} - w + 3]$ $-e^{8} + 13e^{6} - 52e^{4} + 72e^{2} - 26$
23 $[23, 23, w^{3} - 6w]$ $-e^{2}$
27 $[27, 3, w^{3} + w^{2} - 5w - 4]$ $\phantom{-}\frac{1}{4}e^{9} - \frac{5}{2}e^{7} + 5e^{5} + 3e^{3} - \frac{15}{4}e$
41 $[41, 41, -w^{3} + w^{2} + 5w]$ $\phantom{-}e^{9} - 13e^{7} + 52e^{5} - 73e^{3} + 25e$
41 $[41, 41, 2w^{3} - 11w - 4]$ $\phantom{-}\frac{1}{4}e^{9} - \frac{9}{2}e^{7} + 27e^{5} - 59e^{3} + \frac{129}{4}e$
53 $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ $-\frac{3}{2}e^{7} + \frac{35}{2}e^{5} - \frac{109}{2}e^{3} + \frac{83}{2}e$
59 $[59, 59, 2w^{3} - 11w - 2]$ $\phantom{-}\frac{5}{2}e^{8} - \frac{61}{2}e^{6} + \frac{213}{2}e^{4} - \frac{221}{2}e^{2} + 20$
67 $[67, 67, w^{3} - 7w - 1]$ $\phantom{-}\frac{1}{2}e^{8} - \frac{17}{2}e^{6} + \frac{95}{2}e^{4} - \frac{191}{2}e^{2} + 48$
71 $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ $\phantom{-}\frac{5}{4}e^{9} - 16e^{7} + \frac{123}{2}e^{5} - \frac{153}{2}e^{3} + \frac{71}{4}e$
79 $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ $\phantom{-}\frac{3}{4}e^{9} - 10e^{7} + \frac{83}{2}e^{5} - \frac{121}{2}e^{3} + \frac{97}{4}e$
89 $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ $\phantom{-}\frac{3}{2}e^{9} - 19e^{7} + 73e^{5} - 102e^{3} + \frac{111}{2}e$
101 $[101, 101, -2w^{3} + 13w + 6]$ $-e^{8} + 12e^{6} - 41e^{4} + 46e^{2} - 22$
101 $[101, 101, w^{3} + w^{2} - 6w - 3]$ $-\frac{3}{2}e^{8} + \frac{41}{2}e^{6} - \frac{175}{2}e^{4} + \frac{259}{2}e^{2} - 42$
101 $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ $-\frac{3}{4}e^{9} + \frac{19}{2}e^{7} - 36e^{5} + 47e^{3} - \frac{99}{4}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w + 2]$ $1$