Properties

Label 4.4.16357.1-9.1-b
Base field 4.4.16357.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 9, w - 2]$
Dimension $8$
CM no
Base change no

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Base field 4.4.16357.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 9, w - 2]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 98x^{6} + 2825x^{4} - 20232x^{2} + 20736\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}0$
5 $[5, 5, -w^{3} + 5w + 2]$ $-\frac{1}{47520}e^{7} - \frac{19}{4752}e^{5} + \frac{2747}{9504}e^{3} - \frac{623}{220}e$
5 $[5, 5, w - 1]$ $-\frac{2}{495}e^{6} + \frac{23}{99}e^{4} - \frac{248}{99}e^{2} + \frac{346}{55}$
11 $[11, 11, -w^{3} + 5w]$ $-\frac{1}{47520}e^{7} - \frac{19}{4752}e^{5} + \frac{2747}{9504}e^{3} - \frac{843}{220}e$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $-\frac{13}{7920}e^{7} + \frac{83}{792}e^{5} - \frac{2437}{1584}e^{3} + \frac{1469}{330}e$
16 $[16, 2, 2]$ $-\frac{1}{990}e^{6} + \frac{23}{396}e^{4} - \frac{149}{396}e^{2} - \frac{271}{55}$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $\phantom{-}\frac{7}{9504}e^{7} - \frac{127}{4752}e^{5} - \frac{2689}{9504}e^{3} + \frac{235}{132}e$
25 $[25, 5, -w^{2} + w + 3]$ $\phantom{-}0$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $-\frac{1}{23760}e^{7} - \frac{19}{2376}e^{5} + \frac{2747}{4752}e^{3} - \frac{623}{110}e$
31 $[31, 31, -w - 3]$ $\phantom{-}0$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $\phantom{-}\frac{19}{11880}e^{7} - \frac{67}{594}e^{5} + \frac{5029}{2376}e^{3} - \frac{1999}{165}e$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}\frac{1}{660}e^{7} - \frac{1}{22}e^{5} - \frac{151}{132}e^{3} + \frac{1522}{165}e$
43 $[43, 43, w^{3} - 7w - 2]$ $-\frac{4}{495}e^{6} + \frac{46}{99}e^{4} - \frac{496}{99}e^{2} + \frac{692}{55}$
47 $[47, 47, -2w^{3} + 11w + 2]$ $-\frac{31}{9504}e^{7} + \frac{1015}{4752}e^{5} - \frac{31991}{9504}e^{3} + \frac{1681}{132}e$
61 $[61, 61, w^{2} - 3]$ $-\frac{1}{660}e^{7} + \frac{1}{22}e^{5} + \frac{151}{132}e^{3} - \frac{1522}{165}e$
67 $[67, 67, w^{2} + w - 4]$ $\phantom{-}0$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $\phantom{-}\frac{13}{15840}e^{7} - \frac{17}{1584}e^{5} - \frac{4559}{3168}e^{3} + \frac{8651}{660}e$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $\phantom{-}\frac{7}{396}e^{6} - \frac{353}{396}e^{4} + \frac{883}{198}e^{2} + \frac{162}{11}$
97 $[97, 97, -w^{3} + 6w - 3]$ $\phantom{-}\frac{31}{1980}e^{6} - \frac{307}{396}e^{4} + \frac{367}{99}e^{2} + \frac{268}{55}$
97 $[97, 97, -3w^{3} + 16w]$ $-\frac{17}{5280}e^{7} + \frac{39}{176}e^{5} - \frac{4165}{1056}e^{3} + \frac{13463}{660}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $1$