Properties

Label 4.4.18097.1-16.1-d
Base field 4.4.18097.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $9$
CM no
Base change no

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Base field 4.4.18097.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 6x + 4\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $9$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{9} + 2x^{8} - 17x^{7} - 30x^{6} + 86x^{5} + 104x^{4} - 163x^{3} - 66x^{2} + 44x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}e$
4 $[4, 2, w]$ $-1$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $-1$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $\phantom{-}e^{8} + \frac{3}{2}e^{7} - 18e^{6} - \frac{43}{2}e^{5} + 100e^{4} + 61e^{3} - 202e^{2} + \frac{33}{2}e + 42$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $-\frac{3}{4}e^{8} - e^{7} + \frac{51}{4}e^{6} + 14e^{5} - \frac{129}{2}e^{4} - 36e^{3} + \frac{469}{4}e^{2} - 12e - 22$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $-e^{8} - \frac{3}{2}e^{7} + 17e^{6} + \frac{43}{2}e^{5} - 86e^{4} - 61e^{3} + 158e^{2} - \frac{7}{2}e - 32$
27 $[27, 3, -w^{3} + 7w + 1]$ $-\frac{1}{2}e^{8} - e^{7} + \frac{17}{2}e^{6} + 14e^{5} - 43e^{4} - 39e^{3} + \frac{165}{2}e^{2} - 3e - 16$
31 $[31, 31, w + 3]$ $\phantom{-}\frac{7}{4}e^{8} + 3e^{7} - \frac{123}{4}e^{6} - 43e^{5} + \frac{331}{2}e^{4} + 124e^{3} - \frac{1337}{4}e^{2} + 17e + 72$
31 $[31, 31, -w^{2} + 5]$ $-\frac{1}{2}e^{8} - e^{7} + \frac{17}{2}e^{6} + 14e^{5} - 43e^{4} - 39e^{3} + \frac{165}{2}e^{2} - 2e - 16$
37 $[37, 37, w^{2} - 3]$ $-2e^{8} - 3e^{7} + 35e^{6} + 43e^{5} - 186e^{4} - 122e^{3} + 359e^{2} - 20e - 70$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $\phantom{-}e^{8} + 2e^{7} - 18e^{6} - 29e^{5} + 100e^{4} + 90e^{3} - 207e^{2} - 7e + 42$
47 $[47, 47, w^{3} - 5w - 3]$ $\phantom{-}e^{8} + \frac{3}{2}e^{7} - 17e^{6} - \frac{43}{2}e^{5} + 85e^{4} + 62e^{3} - 149e^{2} - \frac{3}{2}e + 26$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $-\frac{5}{2}e^{8} - 4e^{7} + \frac{87}{2}e^{6} + 57e^{5} - 229e^{4} - 161e^{3} + \frac{883}{2}e^{2} - 26e - 86$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $\phantom{-}\frac{3}{4}e^{8} + e^{7} - \frac{55}{4}e^{6} - 14e^{5} + \frac{157}{2}e^{4} + 36e^{3} - \frac{649}{4}e^{2} + 25e + 38$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $\phantom{-}\frac{1}{2}e^{7} - e^{6} - \frac{15}{2}e^{5} + 14e^{4} + 27e^{3} - 48e^{2} + \frac{11}{2}e + 2$
83 $[83, 83, -w^{3} + 5w + 1]$ $-\frac{5}{2}e^{8} - 4e^{7} + \frac{87}{2}e^{6} + 57e^{5} - 230e^{4} - 160e^{3} + \frac{905}{2}e^{2} - 27e - 96$
83 $[83, 83, 2w - 1]$ $-\frac{11}{4}e^{8} - 4e^{7} + \frac{195}{4}e^{6} + 57e^{5} - \frac{531}{2}e^{4} - 156e^{3} + \frac{2125}{4}e^{2} - 59e - 116$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $-\frac{1}{2}e^{8} - e^{7} + \frac{19}{2}e^{6} + 14e^{5} - 57e^{4} - 39e^{3} + \frac{255}{2}e^{2} - 14e - 28$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $-\frac{5}{2}e^{8} - 4e^{7} + \frac{87}{2}e^{6} + 58e^{5} - 229e^{4} - 172e^{3} + \frac{879}{2}e^{2} - 5e - 82$
89 $[89, 89, w^{3} - 5w + 5]$ $-\frac{5}{2}e^{8} - 4e^{7} + \frac{87}{2}e^{6} + 57e^{5} - 229e^{4} - 160e^{3} + \frac{883}{2}e^{2} - 29e - 82$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, w]$ $1$
$4$ $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $1$