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:
\(x^{14} - 23x^{12} + 189x^{10} - 682x^{8} + 1119x^{6} - 766x^{4} + 184x^{2} - 9\) |
Show full eigenvalues Hide large eigenvalues
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 | $[79, 79, w^{2} - 2w - 1]$ | $\phantom{-}\frac{307}{2757}e^{13} - \frac{6914}{2757}e^{11} + \frac{18450}{919}e^{9} - \frac{196153}{2757}e^{7} + \frac{114078}{919}e^{5} - \frac{317122}{2757}e^{3} + \frac{128560}{2757}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w]$ | $-1$ |