Properties

 Base field 4.4.19821.1 Weight [2, 2, 2, 2] Level norm 47 Level $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ Label 4.4.19821.1-47.1-a Dimension 1 CM no Base change no

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Base field 4.4.19821.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 8x^{2} + 6x + 3$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2, 2, 2] Level $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ Label 4.4.19821.1-47.1-a Dimension 1 Is CM no Is base change no Parent newspace dimension 119

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ $\phantom{-}0$
9 $[9, 3, w + 1]$ $\phantom{-}0$
13 $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ $-5$
16 $[16, 2, 2]$ $\phantom{-}3$
17 $[17, 17, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 5]$ $\phantom{-}2$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 5]$ $\phantom{-}0$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 2]$ $-8$
25 $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ $\phantom{-}9$
25 $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$ $-2$
29 $[29, 29, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 4w - 3]$ $\phantom{-}0$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w]$ $\phantom{-}8$
37 $[37, 37, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $-11$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 4]$ $-8$
43 $[43, 43, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w]$ $-7$
47 $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ $\phantom{-}1$
59 $[59, 59, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 4]$ $\phantom{-}10$
59 $[59, 59, \frac{4}{3}w^{3} - \frac{5}{3}w^{2} - 10w + 9]$ $\phantom{-}4$
67 $[67, 67, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w]$ $\phantom{-}13$
71 $[71, 71, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}7$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
47 $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ $-1$