Base field 4.4.9792.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 2x + 7\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[28, 14, -w^{3} + 4w^{2} + 2w - 7]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 41x^{6} + 526x^{4} - 2336x^{2} + 2312\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ | $\phantom{-}1$ |
7 | $[7, 7, w]$ | $\phantom{-}1$ |
7 | $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ | $\phantom{-}\frac{3}{358}e^{6} - \frac{73}{358}e^{4} + \frac{121}{179}e^{2} + \frac{422}{179}$ |
9 | $[9, 3, w^{3} - 4w^{2} - w + 9]$ | $\phantom{-}e$ |
17 | $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ | $-\frac{49}{12172}e^{7} + \frac{1431}{12172}e^{5} - \frac{1913}{3043}e^{3} - \frac{3327}{3043}e$ |
17 | $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ | $\phantom{-}\frac{45}{6086}e^{7} - \frac{1811}{6086}e^{5} + \frac{10407}{3043}e^{3} - \frac{30902}{3043}e$ |
17 | $[17, 17, -w + 2]$ | $-\frac{49}{12172}e^{7} + \frac{1431}{12172}e^{5} - \frac{1913}{3043}e^{3} - \frac{3327}{3043}e$ |
23 | $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ | $\phantom{-}\frac{1}{6086}e^{7} + \frac{95}{6086}e^{5} - \frac{2406}{3043}e^{3} + \frac{21561}{3043}e$ |
23 | $[23, 23, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{47}{12172}e^{7} - \frac{1621}{12172}e^{5} + \frac{4319}{3043}e^{3} - \frac{18234}{3043}e$ |
31 | $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ | $\phantom{-}\frac{11}{358}e^{6} - \frac{387}{358}e^{4} + \frac{1816}{179}e^{2} - \frac{3226}{179}$ |
31 | $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ | $-\frac{7}{179}e^{6} + \frac{230}{179}e^{4} - \frac{1937}{179}e^{2} + \frac{3878}{179}$ |
41 | $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ | $-\frac{47}{12172}e^{7} + \frac{1621}{12172}e^{5} - \frac{4319}{3043}e^{3} + \frac{18234}{3043}e$ |
41 | $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ | $-\frac{93}{6086}e^{7} + \frac{3337}{6086}e^{5} - \frac{16639}{3043}e^{3} + \frac{45809}{3043}e$ |
49 | $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ | $\phantom{-}\frac{3}{358}e^{6} - \frac{73}{358}e^{4} - \frac{58}{179}e^{2} + \frac{2212}{179}$ |
71 | $[71, 71, w^{2} - 2w - 2]$ | $\phantom{-}\frac{24}{3043}e^{7} - \frac{763}{3043}e^{5} + \frac{6232}{3043}e^{3} - \frac{14907}{3043}e$ |
71 | $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ | $-\frac{141}{6086}e^{7} + \frac{4863}{6086}e^{5} - \frac{22871}{3043}e^{3} + \frac{51587}{3043}e$ |
73 | $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ | $\phantom{-}\frac{11}{358}e^{6} - \frac{387}{358}e^{4} + \frac{1637}{179}e^{2} - \frac{1436}{179}$ |
73 | $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ | $\phantom{-}\frac{11}{358}e^{6} - \frac{387}{358}e^{4} + \frac{1637}{179}e^{2} - \frac{1436}{179}$ |
79 | $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ | $\phantom{-}\frac{3}{179}e^{6} - \frac{73}{179}e^{4} + \frac{242}{179}e^{2} + \frac{486}{179}$ |
79 | $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ | $\phantom{-}\frac{3}{179}e^{6} - \frac{73}{179}e^{4} + \frac{242}{179}e^{2} + \frac{486}{179}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ | $-1$ |
$7$ | $[7, 7, w]$ | $-1$ |