Properties

Label 4.4.19429.1-21.1-f
Base field 4.4.19429.1
Weight $[2, 2, 2, 2]$
Level norm $21$
Level $[21, 21, w^{2} - w - 6]$
Dimension $8$
CM no
Base change no

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Base field 4.4.19429.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[21, 21, w^{2} - w - 6]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $37$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} + 2x^{7} - 18x^{6} - 34x^{5} + 53x^{4} + 52x^{3} - 43x^{2} - 7x + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}1$
5 $[5, 5, w]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $-1$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{1666}{5283}e^{7} - \frac{3703}{5283}e^{6} + \frac{29008}{5283}e^{5} + \frac{6977}{587}e^{4} - \frac{71540}{5283}e^{3} - \frac{98834}{5283}e^{2} + \frac{14042}{1761}e + \frac{15760}{5283}$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $\phantom{-}\frac{1484}{5283}e^{7} + \frac{3920}{5283}e^{6} - \frac{24596}{5283}e^{5} - \frac{7448}{587}e^{4} + \frac{43525}{5283}e^{3} + \frac{118048}{5283}e^{2} - \frac{7225}{1761}e - \frac{34460}{5283}$
16 $[16, 2, 2]$ $\phantom{-}\frac{147}{587}e^{7} + \frac{344}{587}e^{6} - \frac{2525}{587}e^{5} - \frac{5765}{587}e^{4} + \frac{5898}{587}e^{3} + \frac{7961}{587}e^{2} - \frac{5478}{587}e - \frac{113}{587}$
17 $[17, 17, -w + 2]$ $-\frac{203}{1761}e^{7} - \frac{503}{1761}e^{6} + \frac{3431}{1761}e^{5} + \frac{2691}{587}e^{4} - \frac{7474}{1761}e^{3} - \frac{6745}{1761}e^{2} + \frac{4059}{587}e - \frac{5686}{1761}$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{1610}{5283}e^{7} - \frac{2957}{5283}e^{6} + \frac{29276}{5283}e^{5} + \frac{5677}{587}e^{4} - \frac{89335}{5283}e^{3} - \frac{83614}{5283}e^{2} + \frac{18853}{1761}e + \frac{6884}{5283}$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $\phantom{-}\frac{238}{5283}e^{7} + \frac{529}{5283}e^{6} - \frac{4144}{5283}e^{5} - \frac{829}{587}e^{4} + \frac{10220}{5283}e^{3} - \frac{9277}{5283}e^{2} - \frac{5528}{1761}e + \frac{9824}{5283}$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $-\frac{899}{1761}e^{7} - \frac{1976}{1761}e^{6} + \frac{15446}{1761}e^{5} + \frac{10911}{587}e^{4} - \frac{36118}{1761}e^{3} - \frac{39682}{1761}e^{2} + \frac{9506}{587}e - \frac{1030}{1761}$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $-\frac{2852}{5283}e^{7} - \frac{5540}{5283}e^{6} + \frac{52766}{5283}e^{5} + \frac{10526}{587}e^{4} - \frac{175609}{5283}e^{3} - \frac{154003}{5283}e^{2} + \frac{56491}{1761}e + \frac{8270}{5283}$
41 $[41, 41, w^{2} - w - 1]$ $\phantom{-}\frac{2002}{5283}e^{7} + \frac{2896}{5283}e^{6} - \frac{37966}{5283}e^{5} - \frac{5385}{587}e^{4} + \frac{139109}{5283}e^{3} + \frac{47513}{5283}e^{2} - \frac{43289}{1761}e + \frac{15512}{5283}$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $\phantom{-}\frac{1769}{5283}e^{7} + \frac{3377}{5283}e^{6} - \frac{32666}{5283}e^{5} - \frac{6475}{587}e^{4} + \frac{108904}{5283}e^{3} + \frac{101545}{5283}e^{2} - \frac{39061}{1761}e - \frac{29444}{5283}$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $\phantom{-}\frac{2944}{5283}e^{7} + \frac{8275}{5283}e^{6} - \frac{46288}{5283}e^{5} - \frac{15429}{587}e^{4} + \frac{45620}{5283}e^{3} + \frac{206177}{5283}e^{2} + \frac{5878}{1761}e - \frac{22852}{5283}$
53 $[53, 53, -w - 3]$ $-\frac{1196}{5283}e^{7} - \frac{3857}{5283}e^{6} + \frac{16163}{5283}e^{5} + \frac{6800}{587}e^{4} + \frac{25712}{5283}e^{3} - \frac{44302}{5283}e^{2} - \frac{27152}{1761}e - \frac{11188}{5283}$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $-\frac{1598}{5283}e^{7} - \frac{5816}{5283}e^{6} + \frac{22541}{5283}e^{5} + \frac{10933}{587}e^{4} + \frac{15908}{5283}e^{3} - \frac{171673}{5283}e^{2} - \frac{10682}{1761}e + \frac{47246}{5283}$
59 $[59, 59, 2w^{2} - 3w - 6]$ $\phantom{-}\frac{3874}{5283}e^{7} + \frac{5947}{5283}e^{6} - \frac{74290}{5283}e^{5} - \frac{11358}{587}e^{4} + \frac{280094}{5283}e^{3} + \frac{151769}{5283}e^{2} - \frac{82715}{1761}e - \frac{17050}{5283}$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $-\frac{7138}{5283}e^{7} - \frac{15466}{5283}e^{6} + \frac{125839}{5283}e^{5} + \frac{29268}{587}e^{4} - \frac{330443}{5283}e^{3} - \frac{422276}{5283}e^{2} + \frac{64943}{1761}e + \frac{58924}{5283}$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $\phantom{-}\frac{10630}{5283}e^{7} + \frac{23494}{5283}e^{6} - \frac{183844}{5283}e^{5} - \frac{43582}{587}e^{4} + \frac{436265}{5283}e^{3} + \frac{525317}{5283}e^{2} - \frac{85319}{1761}e - \frac{41842}{5283}$
79 $[79, 79, w^{2} - 2w - 1]$ $\phantom{-}\frac{7016}{5283}e^{7} + \frac{17237}{5283}e^{6} - \frac{118121}{5283}e^{5} - \frac{32222}{587}e^{4} + \frac{236947}{5283}e^{3} + \frac{434401}{5283}e^{2} - \frac{45550}{1761}e - \frac{66002}{5283}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $-1$
$7$ $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $1$