Properties

Label 4.4.11661.1-16.1-c
Base field 4.4.11661.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $8$
CM no
Base change no

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Base field 4.4.11661.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 23x^{6} + 176x^{4} - 482x^{2} + 289\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w - 2]$ $-\frac{6}{17}e^{7} + \frac{87}{17}e^{5} - \frac{325}{17}e^{3} + \frac{223}{17}e$
3 $[3, 3, w - 1]$ $\phantom{-}\frac{2}{17}e^{7} - \frac{29}{17}e^{5} + \frac{114}{17}e^{3} - \frac{131}{17}e$
16 $[16, 2, 2]$ $-1$
23 $[23, 23, -w^{3} + 4w + 1]$ $-2e^{6} + 28e^{4} - 98e^{2} + 60$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $-\frac{7}{17}e^{7} + \frac{93}{17}e^{5} - \frac{280}{17}e^{3} + \frac{25}{17}e$
25 $[25, 5, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}\frac{15}{17}e^{7} - \frac{209}{17}e^{5} + \frac{719}{17}e^{3} - \frac{362}{17}e$
29 $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ $-\frac{4}{17}e^{7} + \frac{58}{17}e^{5} - \frac{228}{17}e^{3} + \frac{228}{17}e$
29 $[29, 29, w^{3} - w^{2} - 5w + 1]$ $-\frac{4}{17}e^{7} + \frac{58}{17}e^{5} - \frac{228}{17}e^{3} + \frac{228}{17}e$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}e^{6} - 15e^{4} + 59e^{2} - 44$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $-4e^{6} + 57e^{4} - 206e^{2} + 130$
61 $[61, 61, -w^{2} + 2w + 4]$ $-\frac{4}{17}e^{7} + \frac{58}{17}e^{5} - \frac{194}{17}e^{3} + \frac{24}{17}e$
61 $[61, 61, w^{2} - 5]$ $\phantom{-}2e^{3} - 16e$
79 $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ $\phantom{-}\frac{16}{17}e^{7} - \frac{232}{17}e^{5} + \frac{878}{17}e^{3} - \frac{640}{17}e$
79 $[79, 79, -w^{3} + w^{2} + 6w - 4]$ $\phantom{-}\frac{20}{17}e^{7} - \frac{290}{17}e^{5} + \frac{1106}{17}e^{3} - \frac{936}{17}e$
101 $[101, 101, -w^{3} + 3w^{2} + w - 7]$ $\phantom{-}\frac{50}{17}e^{7} - \frac{708}{17}e^{5} + \frac{2544}{17}e^{3} - \frac{1694}{17}e$
101 $[101, 101, w^{3} - 4w - 4]$ $-\frac{2}{17}e^{7} + \frac{12}{17}e^{5} + \frac{90}{17}e^{3} - \frac{328}{17}e$
103 $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ $-2e^{6} + 30e^{4} - 120e^{2} + 96$
103 $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ $\phantom{-}10e^{6} - 142e^{4} + 512e^{2} - 334$
107 $[107, 107, 2w^{2} - 3w - 4]$ $-9e^{6} + 128e^{4} - 463e^{2} + 308$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$