Properties

Base field 6.6.1241125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 25
Level $[25, 5, w^{3} + w^{2} - 4w - 3]$
Label 6.6.1241125.1-25.1-c
Dimension 10
CM no
Base change no

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Base field 6.6.1241125.1

Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2, 2]
Level $[25, 5, w^{3} + w^{2} - 4w - 3]$
Label 6.6.1241125.1-25.1-c
Dimension 10
Is CM no
Is base change no
Parent newspace dimension 19

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} \) \(\mathstrut -\mathstrut 2x^{9} \) \(\mathstrut -\mathstrut 31x^{8} \) \(\mathstrut +\mathstrut 50x^{7} \) \(\mathstrut +\mathstrut 332x^{6} \) \(\mathstrut -\mathstrut 374x^{5} \) \(\mathstrut -\mathstrut 1471x^{4} \) \(\mathstrut +\mathstrut 822x^{3} \) \(\mathstrut +\mathstrut 2372x^{2} \) \(\mathstrut +\mathstrut 168x \) \(\mathstrut -\mathstrut 544\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $\phantom{-}e$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $\phantom{-}\frac{101}{17751}e^{9} - \frac{241}{35502}e^{8} - \frac{3337}{17751}e^{7} + \frac{1875}{11834}e^{6} + \frac{75713}{35502}e^{5} - \frac{13405}{11834}e^{4} - \frac{168194}{17751}e^{3} + \frac{52888}{17751}e^{2} + \frac{224654}{17751}e - \frac{1882}{17751}$
11 $[11, 11, w - 1]$ $-\frac{1823}{142008}e^{9} + \frac{634}{17751}e^{8} + \frac{52573}{142008}e^{7} - \frac{11329}{11834}e^{6} - \frac{61730}{17751}e^{5} + \frac{192109}{23668}e^{4} + \frac{1657265}{142008}e^{3} - \frac{416540}{17751}e^{2} - \frac{298709}{35502}e + \frac{222530}{17751}$
25 $[25, 5, w^{3} + w^{2} - 4w - 3]$ $-1$
29 $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ $\phantom{-}\frac{135}{5917}e^{9} - \frac{1863}{23668}e^{8} - \frac{4008}{5917}e^{7} + \frac{51779}{23668}e^{6} + \frac{80189}{11834}e^{5} - \frac{227473}{11834}e^{4} - \frac{314689}{11834}e^{3} + \frac{1327349}{23668}e^{2} + \frac{384837}{11834}e - \frac{112648}{5917}$
41 $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-\frac{4381}{142008}e^{9} + \frac{2497}{35502}e^{8} + \frac{126935}{142008}e^{7} - \frac{10678}{5917}e^{6} - \frac{297089}{35502}e^{5} + \frac{336221}{23668}e^{4} + \frac{3965635}{142008}e^{3} - \frac{643267}{17751}e^{2} - \frac{764653}{35502}e + \frac{231898}{17751}$
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $-\frac{4969}{284016}e^{9} + \frac{3397}{71004}e^{8} + \frac{146927}{284016}e^{7} - \frac{14367}{11834}e^{6} - \frac{369467}{71004}e^{5} + \frac{444177}{47336}e^{4} + \frac{5800675}{284016}e^{3} - \frac{1637525}{71004}e^{2} - \frac{1414675}{71004}e + \frac{87953}{17751}$
59 $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ $\phantom{-}\frac{10021}{284016}e^{9} - \frac{8671}{71004}e^{8} - \frac{268643}{284016}e^{7} + \frac{18583}{5917}e^{6} + \frac{585863}{71004}e^{5} - \frac{1180077}{47336}e^{4} - \frac{8160871}{284016}e^{3} + \frac{4677371}{71004}e^{2} + \frac{2603023}{71004}e - \frac{452981}{17751}$
59 $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ $-\frac{319}{5917}e^{9} + \frac{795}{5917}e^{8} + \frac{9197}{5917}e^{7} - \frac{20318}{5917}e^{6} - \frac{173225}{11834}e^{5} + \frac{320111}{11834}e^{4} + \frac{300478}{5917}e^{3} - \frac{834037}{11834}e^{2} - \frac{279277}{5917}e + \frac{157510}{5917}$
61 $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ $-\frac{1057}{94672}e^{9} + \frac{1507}{23668}e^{8} + \frac{26335}{94672}e^{7} - \frac{9935}{5917}e^{6} - \frac{54843}{23668}e^{5} + \frac{656715}{47336}e^{4} + \frac{859139}{94672}e^{3} - \frac{912889}{23668}e^{2} - \frac{382203}{23668}e + \frac{93317}{5917}$
61 $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ $-\frac{561}{47336}e^{9} + \frac{245}{11834}e^{8} + \frac{16843}{47336}e^{7} - \frac{5951}{11834}e^{6} - \frac{41557}{11834}e^{5} + \frac{1401}{388}e^{4} + \frac{608987}{47336}e^{3} - \frac{81371}{11834}e^{2} - \frac{158459}{11834}e - \frac{39544}{5917}$
64 $[64, 2, 2]$ $-\frac{665}{17751}e^{9} + \frac{125}{1164}e^{8} + \frac{19312}{17751}e^{7} - \frac{67773}{23668}e^{6} - \frac{370985}{35502}e^{5} + \frac{140447}{5917}e^{4} + \frac{678335}{17751}e^{3} - \frac{4571773}{71004}e^{2} - \frac{1442473}{35502}e + \frac{442135}{17751}$
71 $[71, 71, w^{3} + w^{2} - 5w - 3]$ $\phantom{-}\frac{653}{35502}e^{9} - \frac{736}{17751}e^{8} - \frac{9161}{17751}e^{7} + \frac{6447}{5917}e^{6} + \frac{165043}{35502}e^{5} - \frac{111561}{11834}e^{4} - \frac{266860}{17751}e^{3} + \frac{551540}{17751}e^{2} + \frac{193945}{17751}e - \frac{348176}{17751}$
71 $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ $-\frac{41}{776}e^{9} + \frac{947}{5917}e^{8} + \frac{70387}{47336}e^{7} - \frac{24170}{5917}e^{6} - \frac{163195}{11834}e^{5} + \frac{753209}{23668}e^{4} + \frac{2326275}{47336}e^{3} - \frac{950297}{11834}e^{2} - \frac{602719}{11834}e + \frac{168424}{5917}$
79 $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ $\phantom{-}\frac{113}{11834}e^{9} - \frac{241}{5917}e^{8} - \frac{1630}{5917}e^{7} + \frac{6401}{5917}e^{6} + \frac{34153}{11834}e^{5} - \frac{104777}{11834}e^{4} - \frac{83800}{5917}e^{3} + \frac{142054}{5917}e^{2} + \frac{155010}{5917}e - \frac{70500}{5917}$
81 $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ $\phantom{-}\frac{8147}{142008}e^{9} - \frac{3223}{17751}e^{8} - \frac{225685}{142008}e^{7} + \frac{27208}{5917}e^{6} + \frac{256499}{17751}e^{5} - \frac{838291}{23668}e^{4} - \frac{7221845}{142008}e^{3} + \frac{1563806}{17751}e^{2} + \frac{2042153}{35502}e - \frac{485990}{17751}$
89 $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ $-\frac{2941}{71004}e^{9} + \frac{2419}{17751}e^{8} + \frac{81467}{71004}e^{7} - \frac{42063}{11834}e^{6} - \frac{184124}{17751}e^{5} + \frac{171960}{5917}e^{4} + \frac{2488213}{71004}e^{3} - \frac{2914345}{35502}e^{2} - \frac{544768}{17751}e + \frac{785042}{17751}$
89 $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ $\phantom{-}\frac{8173}{284016}e^{9} - \frac{5011}{71004}e^{8} - \frac{231419}{284016}e^{7} + \frac{10167}{5917}e^{6} + \frac{543881}{71004}e^{5} - \frac{583321}{47336}e^{4} - \frac{8069599}{284016}e^{3} + \frac{1910069}{71004}e^{2} + \frac{2344675}{71004}e - \frac{38453}{17751}$
89 $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ $\phantom{-}\frac{2741}{284016}e^{9} - \frac{743}{71004}e^{8} - \frac{92515}{284016}e^{7} + \frac{1534}{5917}e^{6} + \frac{260059}{71004}e^{5} - \frac{81637}{47336}e^{4} - \frac{4278839}{284016}e^{3} + \frac{82783}{71004}e^{2} + \frac{1112387}{71004}e + \frac{135371}{17751}$
89 $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ $-\frac{163}{47336}e^{9} + \frac{100}{5917}e^{8} + \frac{6221}{47336}e^{7} - \frac{5533}{11834}e^{6} - \frac{21807}{11834}e^{5} + \frac{91985}{23668}e^{4} + \frac{509281}{47336}e^{3} - \frac{50154}{5917}e^{2} - \frac{246267}{11834}e - \frac{19556}{5917}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
25 $[25, 5, w^{3} + w^{2} - 4w - 3]$ $1$