Properties

 Label 4.4.19429.1-25.1-g Base field 4.4.19429.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 25, -2w^{3} + 5w^{2} + 6w - 5]$ Dimension $14$ CM no Base change no

Related objects

• L-function not available

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: $[25, 25, -2w^{3} + 5w^{2} + 6w - 5]$ Dimension: $14$ CM: no Base change: no Newspace dimension: $53$

Hecke eigenvalues ($q$-expansion)

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

 $$x^{14} - 23x^{12} + 189x^{10} - 682x^{8} + 1119x^{6} - 766x^{4} + 184x^{2} - 9$$
Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}e$
5 $[5, 5, w]$ $\phantom{-}0$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $-\frac{127}{1838}e^{12} + \frac{2947}{1838}e^{10} - \frac{12191}{919}e^{8} + \frac{43726}{919}e^{6} - \frac{135891}{1838}e^{4} + \frac{39236}{919}e^{2} - \frac{13115}{1838}$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}\frac{753}{1838}e^{13} - \frac{8581}{919}e^{11} + \frac{69431}{919}e^{9} - \frac{243533}{919}e^{7} + \frac{757103}{1838}e^{5} - \frac{455683}{1838}e^{3} + \frac{34506}{919}e$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $-\frac{469}{1838}e^{13} + \frac{5380}{919}e^{11} - \frac{44000}{919}e^{9} + \frac{157055}{919}e^{7} - \frac{500097}{1838}e^{5} + \frac{307671}{1838}e^{3} - \frac{23641}{919}e$
16 $[16, 2, 2]$ $-\frac{883}{2757}e^{13} + \frac{19976}{2757}e^{11} - \frac{53198}{919}e^{9} + \frac{546937}{2757}e^{7} - \frac{271869}{919}e^{5} + \frac{457720}{2757}e^{3} - \frac{66973}{2757}e$
17 $[17, 17, -w + 2]$ $\phantom{-}\frac{238}{919}e^{12} - \frac{5378}{919}e^{10} + \frac{42805}{919}e^{8} - \frac{144942}{919}e^{6} + \frac{207858}{919}e^{4} - \frac{102953}{919}e^{2} + \frac{12088}{919}$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{34}{919}e^{12} + \frac{637}{919}e^{10} - \frac{3358}{919}e^{8} + \frac{1407}{919}e^{6} + \frac{21770}{919}e^{4} - \frac{35181}{919}e^{2} + \frac{8776}{919}$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $-\frac{48}{919}e^{12} + \frac{2177}{1838}e^{10} - \frac{8687}{919}e^{8} + \frac{29232}{919}e^{6} - \frac{40137}{919}e^{4} + \frac{36299}{1838}e^{2} - \frac{6737}{1838}$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $-\frac{185}{1838}e^{12} + \frac{2179}{919}e^{10} - \frac{18569}{919}e^{8} + \frac{70577}{919}e^{6} - \frac{243091}{1838}e^{4} + \frac{157821}{1838}e^{2} - \frac{10019}{919}$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}\frac{1223}{5514}e^{13} - \frac{27265}{5514}e^{11} + \frac{35259}{919}e^{9} - \frac{338860}{2757}e^{7} + \frac{280787}{1838}e^{5} - \frac{109933}{2757}e^{3} - \frac{57547}{5514}e$
41 $[41, 41, w^{2} - w - 1]$ $-\frac{941}{1838}e^{13} + \frac{21387}{1838}e^{11} - \frac{86175}{919}e^{9} + \frac{300779}{919}e^{7} - \frac{935673}{1838}e^{5} + \frac{292888}{919}e^{3} - \frac{120765}{1838}e$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $-\frac{223}{1838}e^{12} + \frac{2562}{919}e^{10} - \frac{20878}{919}e^{8} + \frac{72958}{919}e^{6} - \frac{214327}{1838}e^{4} + \frac{98229}{1838}e^{2} - \frac{4412}{919}$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $\phantom{-}\frac{81}{919}e^{12} - \frac{1923}{919}e^{10} + \frac{16325}{919}e^{8} - \frac{59438}{919}e^{6} + \frac{86743}{919}e^{4} - \frac{31575}{919}e^{2} - \frac{5717}{919}$
53 $[53, 53, -w - 3]$ $-\frac{524}{919}e^{13} + \frac{23689}{1838}e^{11} - \frac{94297}{919}e^{9} + \frac{319116}{919}e^{7} - \frac{454934}{919}e^{5} + \frac{429731}{1838}e^{3} - \frac{33033}{1838}e$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $\phantom{-}\frac{120}{919}e^{13} - \frac{2951}{919}e^{11} + \frac{26772}{919}e^{9} - \frac{111678}{919}e^{7} + \frac{221191}{919}e^{5} - \frac{190346}{919}e^{3} + \frac{50006}{919}e$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-\frac{257}{2757}e^{13} + \frac{5761}{2757}e^{11} - \frac{15038}{919}e^{9} + \frac{147323}{2757}e^{7} - \frac{65411}{919}e^{5} + \frac{100727}{2757}e^{3} - \frac{48755}{2757}e$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $\phantom{-}\frac{1205}{1838}e^{13} - \frac{13572}{919}e^{11} + \frac{107537}{919}e^{9} - \frac{361868}{919}e^{7} + \frac{1030983}{1838}e^{5} - \frac{501109}{1838}e^{3} + \frac{28176}{919}e$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $\phantom{-}\frac{63}{919}e^{12} - \frac{2685}{1838}e^{10} + \frac{9736}{919}e^{8} - \frac{28258}{919}e^{6} + \frac{32749}{919}e^{4} - \frac{27367}{1838}e^{2} + \frac{4075}{1838}$
79 $[79, 79, w^{2} - 2w - 1]$ $\phantom{-}\frac{307}{2757}e^{13} - \frac{6914}{2757}e^{11} + \frac{18450}{919}e^{9} - \frac{196153}{2757}e^{7} + \frac{114078}{919}e^{5} - \frac{317122}{2757}e^{3} + \frac{128560}{2757}e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w]$ $-1$