Properties

Base field 4.4.13068.1
Weight [2, 2, 2, 2]
Level norm 16
Level $[16, 4, 3w^{3} - 5w^{2} - 15w + 6]$
Label 4.4.13068.1-16.3-e
Dimension 8
CM no
Base change no

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Base field 4.4.13068.1

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

Form

Weight [2, 2, 2, 2]
Level $[16, 4, 3w^{3} - 5w^{2} - 15w + 6]$
Label 4.4.13068.1-16.3-e
Dimension 8
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:
\(x^{8} \) \(\mathstrut -\mathstrut 48x^{6} \) \(\mathstrut +\mathstrut 720x^{4} \) \(\mathstrut -\mathstrut 3456x^{2} \) \(\mathstrut +\mathstrut 64\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}\frac{1}{128}e^{7} - \frac{21}{64}e^{5} + \frac{63}{16}e^{3} - \frac{109}{8}e$
3 $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{64}e^{6} - \frac{9}{16}e^{4} + \frac{37}{8}e^{2} - \frac{5}{2}$
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}0$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $-\frac{1}{64}e^{7} + \frac{21}{32}e^{5} - \frac{63}{8}e^{3} + \frac{105}{4}e$
17 $[17, 17, -w + 2]$ $\phantom{-}e$
29 $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}\frac{1}{64}e^{7} - \frac{51}{64}e^{5} + \frac{51}{4}e^{3} - \frac{511}{8}e$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $\phantom{-}\frac{1}{128}e^{7} - \frac{9}{64}e^{5} - \frac{45}{16}e^{3} + \frac{319}{8}e$
31 $[31, 31, -w^{2} + 2]$ $\phantom{-}\frac{3}{64}e^{6} - \frac{55}{32}e^{4} + \frac{113}{8}e^{2} - \frac{19}{4}$
31 $[31, 31, -w^{3} + 7w + 5]$ $-\frac{1}{64}e^{6} + \frac{19}{32}e^{4} - \frac{39}{8}e^{2} - \frac{25}{4}$
41 $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ $-\frac{1}{128}e^{7} + \frac{3}{64}e^{5} + \frac{97}{16}e^{3} - \frac{525}{8}e$
41 $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ $\phantom{-}\frac{17}{64}e^{5} - \frac{75}{8}e^{3} + \frac{589}{8}e$
67 $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ $\phantom{-}\frac{3}{32}e^{6} - \frac{27}{8}e^{4} + \frac{105}{4}e^{2} + 8$
67 $[67, 67, -w^{2} + 4w + 2]$ $-\frac{3}{32}e^{6} + \frac{27}{8}e^{4} - \frac{105}{4}e^{2} - 10$
83 $[83, 83, 2w^{2} - 5w - 2]$ $-\frac{1}{128}e^{7} + \frac{11}{64}e^{5} + \frac{25}{16}e^{3} - \frac{221}{8}e$
83 $[83, 83, -w^{3} + 8w + 6]$ $\phantom{-}\frac{1}{64}e^{7} - \frac{53}{64}e^{5} + \frac{29}{2}e^{3} - \frac{681}{8}e$
83 $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ $-\frac{1}{32}e^{7} + \frac{95}{64}e^{5} - \frac{175}{8}e^{3} + \frac{811}{8}e$
83 $[83, 83, w^{3} - 2w^{2} - 6w]$ $\phantom{-}\frac{3}{128}e^{7} - \frac{67}{64}e^{5} + \frac{233}{16}e^{3} - \frac{539}{8}e$
97 $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ $\phantom{-}\frac{1}{64}e^{6} - \frac{17}{32}e^{4} + \frac{23}{8}e^{2} + \frac{67}{4}$
97 $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ $-\frac{7}{64}e^{6} + \frac{125}{32}e^{4} - \frac{245}{8}e^{2} + \frac{1}{4}$
97 $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ $\phantom{-}\frac{3}{32}e^{6} - \frac{27}{8}e^{4} + \frac{103}{4}e^{2} + 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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