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: | no |
| Newspace dimension: | $33$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 6x^{5} - 96x^{4} + 496x^{3} + 1032x^{2} - 4400x - 1936\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + 2w^{3} + 2w^{2} - 3w - 3]$ | $-1$ |
| 7 | $[7, 7, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + 2w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}1$ |
| 8 | $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$ | $-\frac{15}{17089}e^{5} + \frac{19}{2972}e^{4} + \frac{1371}{17089}e^{3} - \frac{8345}{17089}e^{2} - \frac{517}{743}e + \frac{17746}{17089}$ |
| 41 | $[41, 41, -\frac{1}{4}w^{4} - \frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 1]$ | $\phantom{-}\frac{141}{1503832}e^{5} + \frac{91}{16346}e^{4} - \frac{9203}{375958}e^{3} - \frac{249541}{375958}e^{2} + \frac{4824}{8173}e + \frac{178238}{17089}$ |
| 41 | $[41, 41, -\frac{1}{2}w^{2} - w + 2]$ | $\phantom{-}\frac{73327}{46618792}e^{5} - \frac{3369}{1013452}e^{4} - \frac{2212971}{11654698}e^{3} + \frac{2054231}{11654698}e^{2} + \frac{1170782}{253363}e - \frac{1613462}{529759}$ |
| 41 | $[41, 41, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + 2w^{2} - 5w - 2]$ | $\phantom{-}\frac{92627}{23309396}e^{5} - \frac{7787}{506726}e^{4} - \frac{2175484}{5827349}e^{3} + \frac{5655649}{5827349}e^{2} + \frac{667207}{253363}e - \frac{1476648}{529759}$ |
| 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 | $[41, 41, \frac{1}{2}w^{2} - w - 2]$ | $\phantom{-}\frac{1179}{1503832}e^{5} - \frac{391}{32692}e^{4} - \frac{20959}{375958}e^{3} + \frac{433131}{375958}e^{2} - \frac{7310}{8173}e - \frac{161806}{17089}$ |
| 41 | $[41, 41, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 1]$ | $-\frac{135821}{46618792}e^{5} - \frac{247}{506726}e^{4} + \frac{3758873}{11654698}e^{3} + \frac{3708341}{11654698}e^{2} - \frac{1309098}{253363}e - \frac{3857858}{529759}$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + w^{2} - 5w + 1]$ | $-\frac{157857}{46618792}e^{5} + \frac{25607}{1013452}e^{4} + \frac{1973979}{5827349}e^{3} - \frac{25599507}{11654698}e^{2} - \frac{1063470}{253363}e + \frac{7559396}{529759}$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + \frac{3}{2}w^{2} - 6w - 2]$ | $\phantom{-}\frac{126975}{46618792}e^{5} - \frac{1195}{253363}e^{4} - \frac{3384143}{11654698}e^{3} + \frac{4958707}{11654698}e^{2} + \frac{1166434}{253363}e - \frac{6019298}{529759}$ |
| 71 | $[71, 71, \frac{1}{4}w^{4} - \frac{1}{2}w^{3} - \frac{5}{2}w^{2} + 3w + 4]$ | $\phantom{-}\frac{12829}{23309396}e^{5} - \frac{5641}{506726}e^{4} - \frac{540145}{11654698}e^{3} + \frac{6174749}{5827349}e^{2} + \frac{328849}{253363}e - \frac{6323350}{529759}$ |
| 71 | $[71, 71, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - 3w + 4]$ | $-\frac{127779}{23309396}e^{5} + \frac{12263}{506726}e^{4} + \frac{5981339}{11654698}e^{3} - \frac{9599115}{5827349}e^{2} - \frac{1337043}{253363}e + \frac{1251266}{529759}$ |
| 71 | $[71, 71, \frac{1}{2}w^{4} - \frac{7}{2}w^{2} + w + 3]$ | $\phantom{-}\frac{144875}{46618792}e^{5} - \frac{1563}{253363}e^{4} - \frac{3741891}{11654698}e^{3} + \frac{1233599}{11654698}e^{2} + \frac{1138914}{253363}e + \frac{2911670}{529759}$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + \frac{5}{2}w^{3} - w^{2} - 5w - 1]$ | $\phantom{-}\frac{3097}{4238072}e^{5} - \frac{1351}{92132}e^{4} - \frac{17867}{529759}e^{3} + \frac{1352123}{1059518}e^{2} - \frac{53298}{23033}e - \frac{4636540}{529759}$ |
| 97 | $[97, 97, \frac{1}{4}w^{5} - \frac{5}{2}w^{3} - \frac{1}{2}w^{2} + 5w]$ | $\phantom{-}\frac{379947}{46618792}e^{5} - \frac{6509}{253363}e^{4} - \frac{9304683}{11654698}e^{3} + \frac{18798735}{11654698}e^{2} + \frac{2046870}{253363}e + \frac{639590}{529759}$ |
| 97 | $[97, 97, -\frac{1}{4}w^{4} + \frac{3}{2}w^{2} + w + 1]$ | $-\frac{73298}{5827349}e^{5} + \frac{13131}{253363}e^{4} + \frac{14106359}{11654698}e^{3} - \frac{21695404}{5827349}e^{2} - \frac{2796443}{253363}e + \frac{7274114}{529759}$ |
| 97 | $[97, 97, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + 2w^{2} - 3w - 4]$ | $-\frac{274977}{46618792}e^{5} + \frac{11459}{1013452}e^{4} + \frac{3756389}{5827349}e^{3} - \frac{7164099}{11654698}e^{2} - \frac{2649870}{253363}e + \frac{4001036}{529759}$ |
| 97 | $[97, 97, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - 2w^{2} - 3w + 4]$ | $\phantom{-}\frac{63509}{46618792}e^{5} - \frac{10941}{1013452}e^{4} - \frac{265469}{5827349}e^{3} + \frac{10329755}{11654698}e^{2} - \frac{1173938}{253363}e - \frac{5004548}{529759}$ |
| 97 | $[97, 97, \frac{1}{4}w^{4} - \frac{3}{2}w^{2} + w - 1]$ | $-\frac{32025}{23309396}e^{5} + \frac{4049}{506726}e^{4} + \frac{856883}{11654698}e^{3} - \frac{2971673}{5827349}e^{2} + \frac{779297}{253363}e + \frac{2225874}{529759}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + 2w^{3} + 2w^{2} - 3w - 3]$ | $1$ |
| $7$ | $[7, 7, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + 2w^{3} - 2w^{2} - 3w + 3]$ | $-1$ |