Base field 4.4.9792.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 7 x^2 + 2 x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[28, 14, -w^3 + 4 w^2 + 2 w - 7]$ |
| 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:
| \(x^8 - 41 x^6 + 526 x^4 - 2336 x^2 + 2312\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^3 - 3 w^2 - 3 w + 4]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w^3 - 3 w^2 - 4 w + 5]$ | $\phantom{-}\frac{3}{358} e^6 - \frac{73}{358} e^4 + \frac{121}{179} e^2 + \frac{422}{179}$ |
| 9 | $[9, 3, w^3 - 4 w^2 - w + 9]$ | $\phantom{-}e$ |
| 17 | $[17, 17, 2 w^3 - 6 w^2 - 7 w + 8]$ | $-\frac{49}{12172} e^7 + \frac{1431}{12172} e^5 - \frac{1913}{3043} e^3 - \frac{3327}{3043} e$ |
| 17 | $[17, 17, -w^3 + 3 w^2 + 4 w - 3]$ | $\phantom{-}\frac{45}{6086} e^7 - \frac{1811}{6086} e^5 + \frac{10407}{3043} e^3 - \frac{30902}{3043} e$ |
| 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 | $[23, 23, 2 w^3 - 7 w^2 - 4 w + 12]$ | $\phantom{-}\frac{1}{6086} e^7 + \frac{95}{6086} e^5 - \frac{2406}{3043} e^3 + \frac{21561}{3043} e$ |
| 23 | $[23, 23, -w^2 + 2 w + 3]$ | $\phantom{-}\frac{47}{12172} e^7 - \frac{1621}{12172} e^5 + \frac{4319}{3043} e^3 - \frac{18234}{3043} e$ |
| 31 | $[31, 31, -2 w^3 + 7 w^2 + 5 w - 12]$ | $\phantom{-}\frac{11}{358} e^6 - \frac{387}{358} e^4 + \frac{1816}{179} e^2 - \frac{3226}{179}$ |
| 31 | $[31, 31, -w^3 + 4 w^2 + 2 w - 8]$ | $-\frac{7}{179} e^6 + \frac{230}{179} e^4 - \frac{1937}{179} e^2 + \frac{3878}{179}$ |
| 41 | $[41, 41, 3 w^3 - 10 w^2 - 7 w + 16]$ | $-\frac{47}{12172} e^7 + \frac{1621}{12172} e^5 - \frac{4319}{3043} e^3 + \frac{18234}{3043} e$ |
| 41 | $[41, 41, 2 w^3 - 7 w^2 - 5 w + 10]$ | $-\frac{93}{6086} e^7 + \frac{3337}{6086} e^5 - \frac{16639}{3043} e^3 + \frac{45809}{3043} e$ |
| 49 | $[49, 7, 2 w^3 - 6 w^2 - 6 w + 9]$ | $\phantom{-}\frac{3}{358} e^6 - \frac{73}{358} e^4 - \frac{58}{179} e^2 + \frac{2212}{179}$ |
| 71 | $[71, 71, w^2 - 2 w - 2]$ | $\phantom{-}\frac{24}{3043} e^7 - \frac{763}{3043} e^5 + \frac{6232}{3043} e^3 - \frac{14907}{3043} e$ |
| 71 | $[71, 71, 2 w^3 - 7 w^2 - 4 w + 13]$ | $-\frac{141}{6086} e^7 + \frac{4863}{6086} e^5 - \frac{22871}{3043} e^3 + \frac{51587}{3043} e$ |
| 73 | $[73, 73, 3 w^3 - 11 w^2 - 5 w + 19]$ | $\phantom{-}\frac{11}{358} e^6 - \frac{387}{358} e^4 + \frac{1637}{179} e^2 - \frac{1436}{179}$ |
| 73 | $[73, 73, -4 w^3 + 13 w^2 + 10 w - 17]$ | $\phantom{-}\frac{11}{358} e^6 - \frac{387}{358} e^4 + \frac{1637}{179} e^2 - \frac{1436}{179}$ |
| 79 | $[79, 79, 3 w^3 - 9 w^2 - 10 w + 13]$ | $\phantom{-}\frac{3}{179} e^6 - \frac{73}{179} e^4 + \frac{242}{179} e^2 + \frac{486}{179}$ |
| 79 | $[79, 79, -2 w^3 + 6 w^2 + 5 w - 8]$ | $\phantom{-}\frac{3}{179} e^6 - \frac{73}{179} e^4 + \frac{242}{179} e^2 + \frac{486}{179}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^3 - 3 w^2 - 3 w + 4]$ | $-1$ |
| $7$ | $[7, 7, w]$ | $-1$ |