Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 58x^{6} + 553x^{4} + 1168x^{2} + 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{221}{26096}e^{7} + \frac{6289}{13048}e^{5} + \frac{109085}{26096}e^{3} + \frac{22233}{3262}e$ |
| 3 | $[3, 3, w]$ | $-\frac{47}{14912}e^{7} - \frac{1367}{7456}e^{5} - \frac{26615}{14912}e^{3} - \frac{8043}{1864}e$ |
| 5 | $[5, 5, -w + 5]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{221}{26096}e^{7} + \frac{6289}{13048}e^{5} + \frac{109085}{26096}e^{3} + \frac{18971}{3262}e$ |
| 7 | $[7, 7, w + 4]$ | $-\frac{221}{26096}e^{7} - \frac{6289}{13048}e^{5} - \frac{109085}{26096}e^{3} - \frac{18971}{3262}e$ |
| 13 | $[13, 13, w + 2]$ | $\phantom{-}\frac{195}{13048}e^{7} + \frac{5741}{6524}e^{5} + \frac{116591}{13048}e^{3} + \frac{33241}{1631}e$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{195}{13048}e^{7} - \frac{5741}{6524}e^{5} - \frac{116591}{13048}e^{3} - \frac{33241}{1631}e$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}\frac{221}{13048}e^{7} + \frac{6289}{6524}e^{5} + \frac{109085}{13048}e^{3} + \frac{22233}{1631}e$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}\frac{221}{13048}e^{7} + \frac{6289}{6524}e^{5} + \frac{109085}{13048}e^{3} + \frac{22233}{1631}e$ |
| 19 | $[19, 19, w + 7]$ | $\phantom{-}\frac{20}{1631}e^{6} + \frac{1094}{1631}e^{4} + \frac{7776}{1631}e^{2} + \frac{8790}{1631}$ |
| 19 | $[19, 19, -w + 7]$ | $\phantom{-}\frac{20}{1631}e^{6} + \frac{1094}{1631}e^{4} + \frac{7776}{1631}e^{2} + \frac{8790}{1631}$ |
| 29 | $[29, 29, -w - 1]$ | $\phantom{-}\frac{13}{3262}e^{6} + \frac{274}{1631}e^{4} - \frac{3753}{3262}e^{2} - \frac{15492}{1631}$ |
| 29 | $[29, 29, w - 1]$ | $-\frac{13}{3262}e^{6} - \frac{274}{1631}e^{4} + \frac{3753}{3262}e^{2} + \frac{15492}{1631}$ |
| 37 | $[37, 37, w + 17]$ | $-\frac{52}{1631}e^{7} - \frac{6015}{3262}e^{5} - \frac{56419}{3262}e^{3} - \frac{52212}{1631}e$ |
| 37 | $[37, 37, w + 20]$ | $\phantom{-}\frac{52}{1631}e^{7} + \frac{6015}{3262}e^{5} + \frac{56419}{3262}e^{3} + \frac{52212}{1631}e$ |
| 71 | $[71, 71, 2w - 7]$ | $-\frac{37}{1631}e^{6} - \frac{2187}{1631}e^{4} - \frac{21562}{1631}e^{2} - \frac{25232}{1631}$ |
| 71 | $[71, 71, -2w - 7]$ | $\phantom{-}\frac{37}{1631}e^{6} + \frac{2187}{1631}e^{4} + \frac{21562}{1631}e^{2} + \frac{25232}{1631}$ |
| 83 | $[83, 83, w + 14]$ | $\phantom{-}\frac{47}{3728}e^{7} + \frac{1367}{1864}e^{5} + \frac{26615}{3728}e^{3} + \frac{8043}{466}e$ |
| 83 | $[83, 83, w + 69]$ | $\phantom{-}\frac{47}{3728}e^{7} + \frac{1367}{1864}e^{5} + \frac{26615}{3728}e^{3} + \frac{8043}{466}e$ |
| 101 | $[101, 101, -7w + 37]$ | $-\frac{87}{3262}e^{6} - \frac{2461}{1631}e^{4} - \frac{39371}{3262}e^{2} - \frac{9740}{1631}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $\frac{47}{14912}e^{7} + \frac{1367}{7456}e^{5} + \frac{26615}{14912}e^{3} + \frac{8043}{1864}e$ |