Properties

Base field 4.4.19821.1
Weight [2, 2, 2, 2]
Level norm 48
Level $[48, 6, 2w]$
Label 4.4.19821.1-48.1-b
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 $[48, 6, 2w]$
Label 4.4.19821.1-48.1-b
Dimension 1
Is CM no
Is base change no
Parent newspace dimension 84

Hecke eigenvalues ($q$-expansion)

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
16 $[16, 2, 2]$ $-1$