Base field 6.6.1229312.1
Generator \(w\), with minimal polynomial \(x^{6} - 10x^{4} + 24x^{2} - 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[49, 7, -\frac{1}{2}w^{4} + \frac{7}{2}w^{2} - 3]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $33$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 10x^{5} - 88x^{4} + 816x^{3} + 840x^{2} - 2096x - 2000\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + 2w^{3} + 2w^{2} - 3w - 3]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + 2w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}1$ |
| 8 | $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$ | $-\frac{1}{137}e^{5} + \frac{47}{548}e^{4} + \frac{76}{137}e^{3} - \frac{949}{137}e^{2} + \frac{33}{137}e + \frac{1730}{137}$ |
| 41 | $[41, 41, -\frac{1}{4}w^{4} - \frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 1]$ | $\phantom{-}\frac{7157}{695960}e^{5} - \frac{9403}{86995}e^{4} - \frac{145847}{173990}e^{3} + \frac{1526577}{173990}e^{2} + \frac{213738}{86995}e - \frac{265118}{17399}$ |
| 41 | $[41, 41, -\frac{1}{2}w^{2} - w + 2]$ | $-\frac{2077}{695960}e^{5} + \frac{7767}{347980}e^{4} + \frac{49327}{173990}e^{3} - \frac{321347}{173990}e^{2} - \frac{321688}{86995}e + \frac{149802}{17399}$ |
| 41 | $[41, 41, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + 2w^{2} - 5w - 2]$ | $\phantom{-}e$ |
| 41 | $[41, 41, \frac{1}{4}w^{5} - \frac{1}{4}w^{4} - \frac{5}{2}w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}e$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} - w - 2]$ | $-\frac{2077}{695960}e^{5} + \frac{7767}{347980}e^{4} + \frac{49327}{173990}e^{3} - \frac{321347}{173990}e^{2} - \frac{321688}{86995}e + \frac{149802}{17399}$ |
| 41 | $[41, 41, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 1]$ | $\phantom{-}\frac{7157}{695960}e^{5} - \frac{9403}{86995}e^{4} - \frac{145847}{173990}e^{3} + \frac{1526577}{173990}e^{2} + \frac{213738}{86995}e - \frac{265118}{17399}$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + w^{2} - 5w + 1]$ | $\phantom{-}\frac{969}{139192}e^{5} - \frac{5299}{69596}e^{4} - \frac{9274}{17399}e^{3} + \frac{215613}{34798}e^{2} - \frac{2884}{17399}e - \frac{205676}{17399}$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + \frac{3}{2}w^{2} - 6w - 2]$ | $-\frac{1869}{695960}e^{5} + \frac{4437}{173990}e^{4} + \frac{41539}{173990}e^{3} - \frac{376119}{173990}e^{2} - \frac{160886}{86995}e + \frac{186838}{17399}$ |
| 71 | $[71, 71, \frac{1}{4}w^{4} - \frac{1}{2}w^{3} - \frac{5}{2}w^{2} + 3w + 4]$ | $\phantom{-}\frac{263}{86995}e^{5} - \frac{3056}{86995}e^{4} - \frac{45319}{173990}e^{3} + \frac{251642}{86995}e^{2} + \frac{154351}{86995}e - \frac{26882}{17399}$ |
| 71 | $[71, 71, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - 3w + 4]$ | $\phantom{-}\frac{263}{86995}e^{5} - \frac{3056}{86995}e^{4} - \frac{45319}{173990}e^{3} + \frac{251642}{86995}e^{2} + \frac{154351}{86995}e - \frac{26882}{17399}$ |
| 71 | $[71, 71, \frac{1}{2}w^{4} - \frac{7}{2}w^{2} + w + 3]$ | $-\frac{1869}{695960}e^{5} + \frac{4437}{173990}e^{4} + \frac{41539}{173990}e^{3} - \frac{376119}{173990}e^{2} - \frac{160886}{86995}e + \frac{186838}{17399}$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + \frac{5}{2}w^{3} - w^{2} - 5w - 1]$ | $\phantom{-}\frac{969}{139192}e^{5} - \frac{5299}{69596}e^{4} - \frac{9274}{17399}e^{3} + \frac{215613}{34798}e^{2} - \frac{2884}{17399}e - \frac{205676}{17399}$ |
| 97 | $[97, 97, \frac{1}{4}w^{5} - \frac{5}{2}w^{3} - \frac{1}{2}w^{2} + 5w]$ | $\phantom{-}\frac{8237}{695960}e^{5} - \frac{20951}{173990}e^{4} - \frac{159517}{173990}e^{3} + \frac{1670467}{173990}e^{2} - \frac{42112}{86995}e - \frac{289634}{17399}$ |
| 97 | $[97, 97, -\frac{1}{4}w^{4} + \frac{3}{2}w^{2} + w + 1]$ | $-\frac{3793}{347980}e^{5} + \frac{20383}{173990}e^{4} + \frac{140161}{173990}e^{3} - \frac{826423}{86995}e^{2} + \frac{357181}{86995}e + \frac{384470}{17399}$ |
| 97 | $[97, 97, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + 2w^{2} - 3w - 4]$ | $\phantom{-}\frac{4429}{695960}e^{5} - \frac{28709}{347980}e^{4} - \frac{38582}{86995}e^{3} + \frac{1187609}{173990}e^{2} - \frac{336024}{86995}e - \frac{279748}{17399}$ |
| 97 | $[97, 97, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - 2w^{2} - 3w + 4]$ | $\phantom{-}\frac{4429}{695960}e^{5} - \frac{28709}{347980}e^{4} - \frac{38582}{86995}e^{3} + \frac{1187609}{173990}e^{2} - \frac{336024}{86995}e - \frac{279748}{17399}$ |
| 97 | $[97, 97, \frac{1}{4}w^{4} - \frac{3}{2}w^{2} + w - 1]$ | $-\frac{3793}{347980}e^{5} + \frac{20383}{173990}e^{4} + \frac{140161}{173990}e^{3} - \frac{826423}{86995}e^{2} + \frac{357181}{86995}e + \frac{384470}{17399}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + 2w^{3} + 2w^{2} - 3w - 3]$ | $-1$ |
| $7$ | $[7, 7, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + 2w^{3} - 2w^{2} - 3w + 3]$ | $-1$ |