Base field 5.5.180769.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 7x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 37x^{8} + 454x^{6} - 1984x^{4} + 1888x^{2} - 128\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $\phantom{-}\frac{1}{344}e^{8} - \frac{1}{8}e^{6} + \frac{135}{86}e^{4} - \frac{489}{86}e^{2} + \frac{112}{43}$ |
5 | $[5, 5, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $-\frac{11}{1376}e^{9} + \frac{9}{32}e^{7} - \frac{2239}{688}e^{5} + \frac{2281}{172}e^{3} - \frac{480}{43}e$ |
7 | $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}1$ |
19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $-\frac{1}{688}e^{9} + \frac{1}{16}e^{7} - \frac{135}{172}e^{5} + \frac{403}{172}e^{3} + \frac{202}{43}e$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}2$ |
32 | $[32, 2, 2]$ | $\phantom{-}\frac{9}{688}e^{8} - \frac{7}{16}e^{6} + \frac{1699}{344}e^{4} - \frac{853}{43}e^{2} + \frac{461}{43}$ |
37 | $[37, 37, -w^{4} + 2w^{3} + 3w^{2} - 7w + 4]$ | $\phantom{-}\frac{5}{344}e^{9} - \frac{1}{2}e^{7} + \frac{1969}{344}e^{5} - \frac{3987}{172}e^{3} + \frac{646}{43}e$ |
41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $-\frac{1}{688}e^{9} + \frac{1}{16}e^{7} - \frac{135}{172}e^{5} + \frac{403}{172}e^{3} + \frac{202}{43}e$ |
43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 5w - 3]$ | $\phantom{-}\frac{13}{688}e^{9} - \frac{11}{16}e^{7} + \frac{2779}{344}e^{5} - \frac{1342}{43}e^{3} + \frac{642}{43}e$ |
43 | $[43, 43, -w^{2} + w + 3]$ | $-\frac{1}{86}e^{8} + \frac{1}{4}e^{6} - \frac{177}{172}e^{4} - \frac{237}{86}e^{2} + \frac{240}{43}$ |
47 | $[47, 47, 2w^{4} - 3w^{3} - 9w^{2} + 8w + 3]$ | $-\frac{17}{688}e^{9} + \frac{15}{16}e^{7} - \frac{4031}{344}e^{5} + \frac{4393}{86}e^{3} - \frac{1855}{43}e$ |
61 | $[61, 61, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 2]$ | $-\frac{1}{43}e^{9} + \frac{7}{8}e^{7} - \frac{3761}{344}e^{5} + \frac{8383}{172}e^{3} - \frac{1971}{43}e$ |
79 | $[79, 79, w^{2} - w - 5]$ | $-\frac{9}{344}e^{9} + e^{7} - \frac{4301}{344}e^{5} + \frac{9189}{172}e^{3} - \frac{1567}{43}e$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}\frac{5}{688}e^{9} - \frac{5}{16}e^{7} + \frac{761}{172}e^{5} - \frac{3993}{172}e^{3} + \frac{1570}{43}e$ |
79 | $[79, 79, -2w^{4} + 4w^{3} + 7w^{2} - 14w + 2]$ | $\phantom{-}\frac{1}{32}e^{9} - \frac{37}{32}e^{7} + \frac{227}{16}e^{5} - 61e^{3} + 46e$ |
97 | $[97, 97, w^{3} - 6w]$ | $\phantom{-}\frac{3}{344}e^{9} - \frac{3}{8}e^{7} + \frac{224}{43}e^{5} - \frac{1099}{43}e^{3} + \frac{1325}{43}e$ |
101 | $[101, 101, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $-\frac{9}{344}e^{9} + e^{7} - \frac{4301}{344}e^{5} + \frac{9361}{172}e^{3} - \frac{2169}{43}e$ |
101 | $[101, 101, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 1]$ | $-\frac{1}{344}e^{9} + \frac{1}{8}e^{7} - \frac{135}{86}e^{5} + \frac{489}{86}e^{3} - \frac{69}{43}e$ |
107 | $[107, 107, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 2]$ | $\phantom{-}\frac{5}{344}e^{8} - \frac{3}{8}e^{6} + \frac{447}{172}e^{4} - \frac{169}{43}e^{2} + \frac{130}{43}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7,7,w^{4}-w^{3}-5w^{2}+3w+3]$ | $-1$ |