# Properties

 Base field 4.4.15952.1 Weight [2, 2, 2, 2] Level norm 17 Level $[17, 17, -w^{2} - w + 3]$ Label 4.4.15952.1-17.2-b Dimension 12 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 $[17, 17, -w^{2} - w + 3]$ Label 4.4.15952.1-17.2-b Dimension 12 Is CM no Is base change no Parent newspace dimension 42

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{12}$$ $$\mathstrut -\mathstrut 15x^{10}$$ $$\mathstrut +\mathstrut 82x^{8}$$ $$\mathstrut -\mathstrut 203x^{6}$$ $$\mathstrut +\mathstrut 220x^{4}$$ $$\mathstrut -\mathstrut 76x^{2}$$ $$\mathstrut +\mathstrut 4$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -w^{3} + w^{2} + 5w - 2]$ $-\frac{1}{2}e^{11} + \frac{13}{2}e^{9} - 29e^{7} + \frac{111}{2}e^{5} - 45e^{3} + 13e$
11 $[11, 11, -w^{3} + 5w + 1]$ $-\frac{1}{2}e^{11} + \frac{13}{2}e^{9} - 28e^{7} + \frac{91}{2}e^{5} - 18e^{3} - 7e$
11 $[11, 11, -w + 2]$ $\phantom{-}2e^{10} - 25e^{8} + 102e^{6} - 157e^{4} + 70e^{2} - 8$
13 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $\phantom{-}\frac{1}{2}e^{11} - \frac{11}{2}e^{9} + 17e^{7} - \frac{19}{2}e^{5} - 20e^{3} + 11e$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $\phantom{-}e^{11} - 13e^{9} + 57e^{7} - 102e^{5} + 71e^{3} - 20e$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}1$
23 $[23, 23, w^{3} - 6w]$ $-2e^{10} + 25e^{8} - 101e^{6} + 148e^{4} - 51e^{2}$
27 $[27, 3, w^{3} + w^{2} - 5w - 4]$ $-e^{9} + 12e^{7} - 46e^{5} + 64e^{3} - 20e$
41 $[41, 41, -w^{3} + w^{2} + 5w]$ $-\frac{3}{2}e^{11} + \frac{39}{2}e^{9} - 85e^{7} + \frac{295}{2}e^{5} - 91e^{3} + 19e$
41 $[41, 41, 2w^{3} - 11w - 4]$ $\phantom{-}2e^{11} - 28e^{9} + 138e^{7} - 293e^{5} + 249e^{3} - 54e$
53 $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ $-e^{11} + 12e^{9} - 43e^{7} + 37e^{5} + 39e^{3} - 24e$
59 $[59, 59, 2w^{3} - 11w - 2]$ $-2e^{10} + 26e^{8} - 115e^{6} + 211e^{4} - 146e^{2} + 20$
67 $[67, 67, w^{3} - 7w - 1]$ $-3e^{10} + 37e^{8} - 150e^{6} + 240e^{4} - 132e^{2} + 12$
71 $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ $\phantom{-}\frac{5}{2}e^{11} - \frac{61}{2}e^{9} + 120e^{7} - \frac{349}{2}e^{5} + 60e^{3} + 19e$
79 $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ $\phantom{-}3e^{11} - 38e^{9} + 158e^{7} - 248e^{5} + 108e^{3} - 2e$
89 $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ $\phantom{-}e^{9} - 13e^{7} + 56e^{5} - 93e^{3} + 48e$
101 $[101, 101, -2w^{3} + 13w + 6]$ $-3e^{10} + 37e^{8} - 144e^{6} + 185e^{4} - 19e^{2} - 6$
101 $[101, 101, w^{3} + w^{2} - 6w - 3]$ $\phantom{-}3e^{10} - 38e^{8} + 159e^{6} - 256e^{4} + 122e^{2} - 10$
101 $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ $-\frac{3}{2}e^{11} + \frac{31}{2}e^{9} - 39e^{7} - \frac{33}{2}e^{5} + 116e^{3} - 41e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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