Base field \(\Q(\sqrt{393}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 98\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, -842w + 8767]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 18x^{8} + 115x^{6} - 314x^{4} + 335x^{2} - 91\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -17w - 160]$ | $-e$ |
| 2 | $[2, 2, -17w + 177]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -842w + 8767]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -2w + 21]$ | $-\frac{4}{19}e^{8} + \frac{51}{19}e^{6} - \frac{178}{19}e^{4} + \frac{141}{19}e^{2} - \frac{6}{19}$ |
| 7 | $[7, 7, 2w + 19]$ | $-\frac{4}{19}e^{8} + \frac{51}{19}e^{6} - \frac{178}{19}e^{4} + \frac{141}{19}e^{2} - \frac{6}{19}$ |
| 13 | $[13, 13, -12w - 113]$ | $\phantom{-}\frac{10}{19}e^{8} - \frac{137}{19}e^{6} + \frac{559}{19}e^{4} - \frac{723}{19}e^{2} + \frac{224}{19}$ |
| 13 | $[13, 13, 12w - 125]$ | $\phantom{-}\frac{10}{19}e^{8} - \frac{137}{19}e^{6} + \frac{559}{19}e^{4} - \frac{723}{19}e^{2} + \frac{224}{19}$ |
| 17 | $[17, 17, 182w - 1895]$ | $-\frac{5}{19}e^{9} + \frac{78}{19}e^{7} - \frac{403}{19}e^{5} + \frac{789}{19}e^{3} - \frac{416}{19}e$ |
| 17 | $[17, 17, 182w + 1713]$ | $\phantom{-}\frac{5}{19}e^{9} - \frac{78}{19}e^{7} + \frac{403}{19}e^{5} - \frac{789}{19}e^{3} + \frac{416}{19}e$ |
| 23 | $[23, 23, -512w - 4819]$ | $-\frac{3}{19}e^{9} + \frac{43}{19}e^{7} - \frac{181}{19}e^{5} + \frac{196}{19}e^{3} + \frac{43}{19}e$ |
| 23 | $[23, 23, 512w - 5331]$ | $\phantom{-}\frac{3}{19}e^{9} - \frac{43}{19}e^{7} + \frac{181}{19}e^{5} - \frac{196}{19}e^{3} - \frac{43}{19}e$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{7}{19}e^{8} - \frac{94}{19}e^{6} + \frac{359}{19}e^{4} - \frac{356}{19}e^{2} - \frac{94}{19}$ |
| 29 | $[29, 29, 22w - 229]$ | $-\frac{3}{19}e^{9} + \frac{43}{19}e^{7} - \frac{200}{19}e^{5} + \frac{367}{19}e^{3} - \frac{242}{19}e$ |
| 29 | $[29, 29, 22w + 207]$ | $\phantom{-}\frac{3}{19}e^{9} - \frac{43}{19}e^{7} + \frac{200}{19}e^{5} - \frac{367}{19}e^{3} + \frac{242}{19}e$ |
| 43 | $[43, 43, 114w + 1073]$ | $-\frac{21}{19}e^{8} + \frac{301}{19}e^{6} - \frac{1343}{19}e^{4} + \frac{2018}{19}e^{2} - \frac{649}{19}$ |
| 43 | $[43, 43, 114w - 1187]$ | $-\frac{21}{19}e^{8} + \frac{301}{19}e^{6} - \frac{1343}{19}e^{4} + \frac{2018}{19}e^{2} - \frac{649}{19}$ |
| 47 | $[47, 47, 8w - 83]$ | $\phantom{-}\frac{9}{19}e^{9} - \frac{129}{19}e^{7} + \frac{562}{19}e^{5} - \frac{740}{19}e^{3} + \frac{4}{19}e$ |
| 47 | $[47, 47, -8w - 75]$ | $-\frac{9}{19}e^{9} + \frac{129}{19}e^{7} - \frac{562}{19}e^{5} + \frac{740}{19}e^{3} - \frac{4}{19}e$ |
| 61 | $[61, 61, -1172w - 11031]$ | $\phantom{-}\frac{9}{19}e^{8} - \frac{110}{19}e^{6} + \frac{353}{19}e^{4} - \frac{208}{19}e^{2} - \frac{91}{19}$ |
| 61 | $[61, 61, 1172w - 12203]$ | $\phantom{-}\frac{9}{19}e^{8} - \frac{110}{19}e^{6} + \frac{353}{19}e^{4} - \frac{208}{19}e^{2} - \frac{91}{19}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -842w + 8767]$ | $-1$ |