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: | $[6,6,5w - 52]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 2x^{9} - 14x^{8} + 24x^{7} + 71x^{6} - 89x^{5} - 162x^{4} + 96x^{3} + 154x^{2} + 12x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -17w - 160]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -17w + 177]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -842w + 8767]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -2w + 21]$ | $-\frac{3}{2}e^{9} + \frac{5}{2}e^{8} + 18e^{7} - 27e^{6} - \frac{135}{2}e^{5} + 85e^{4} + \frac{167}{2}e^{3} - 70e^{2} - 28e + 5$ |
| 7 | $[7, 7, 2w + 19]$ | $\phantom{-}\frac{3}{4}e^{9} - \frac{1}{2}e^{8} - \frac{19}{2}e^{7} + 4e^{6} + \frac{149}{4}e^{5} - \frac{19}{4}e^{4} - \frac{85}{2}e^{3} - 11e^{2} - \frac{7}{2}e - 2$ |
| 13 | $[13, 13, -12w - 113]$ | $-\frac{3}{4}e^{9} - \frac{5}{2}e^{8} + \frac{23}{2}e^{7} + 34e^{6} - \frac{213}{4}e^{5} - \frac{585}{4}e^{4} + \frac{125}{2}e^{3} + 197e^{2} + \frac{91}{2}e - 9$ |
| 13 | $[13, 13, 12w - 125]$ | $\phantom{-}\frac{3}{4}e^{9} + \frac{1}{2}e^{8} - \frac{21}{2}e^{7} - 8e^{6} + \frac{185}{4}e^{5} + \frac{157}{4}e^{4} - \frac{123}{2}e^{3} - 58e^{2} - \frac{11}{2}e - 1$ |
| 17 | $[17, 17, 182w - 1895]$ | $\phantom{-}\frac{11}{4}e^{9} - \frac{5}{2}e^{8} - \frac{69}{2}e^{7} + 23e^{6} + \frac{541}{4}e^{5} - \frac{199}{4}e^{4} - \frac{329}{2}e^{3} - 4e^{2} + \frac{31}{2}e + 1$ |
| 17 | $[17, 17, 182w + 1713]$ | $\phantom{-}\frac{1}{4}e^{9} - e^{8} - \frac{5}{2}e^{7} + 12e^{6} + \frac{27}{4}e^{5} - \frac{179}{4}e^{4} - 5e^{3} + 52e^{2} + \frac{15}{2}e - 4$ |
| 23 | $[23, 23, -512w - 4819]$ | $-\frac{7}{4}e^{9} + \frac{9}{2}e^{8} + \frac{39}{2}e^{7} - 51e^{6} - \frac{261}{4}e^{5} + \frac{695}{4}e^{4} + \frac{141}{2}e^{3} - 167e^{2} - \frac{83}{2}e + 5$ |
| 23 | $[23, 23, 512w - 5331]$ | $-3e^{9} + \frac{5}{2}e^{8} + 37e^{7} - 21e^{6} - 140e^{5} + \frac{65}{2}e^{4} + \frac{301}{2}e^{3} + 39e^{2} + 19e - 1$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{3}{2}e^{8} - e^{7} - 19e^{6} + 8e^{5} + \frac{151}{2}e^{4} - \frac{21}{2}e^{3} - 93e^{2} - 19e + 7$ |
| 29 | $[29, 29, 22w - 229]$ | $-e^{9} + \frac{5}{2}e^{8} + 11e^{7} - 28e^{6} - 35e^{5} + \frac{187}{2}e^{4} + \frac{57}{2}e^{3} - 89e^{2} - 3e + 14$ |
| 29 | $[29, 29, 22w + 207]$ | $\phantom{-}\frac{7}{4}e^{9} - 3e^{8} - \frac{41}{2}e^{7} + 32e^{6} + \frac{289}{4}e^{5} - \frac{389}{4}e^{4} - 72e^{3} + 69e^{2} + \frac{11}{2}e + 2$ |
| 43 | $[43, 43, 114w + 1073]$ | $\phantom{-}2e^{9} - \frac{9}{2}e^{8} - 22e^{7} + 50e^{6} + 70e^{5} - \frac{331}{2}e^{4} - \frac{117}{2}e^{3} + 153e^{2} + 15e - 11$ |
| 43 | $[43, 43, 114w - 1187]$ | $-\frac{1}{2}e^{9} + 5e^{8} + 2e^{7} - 61e^{6} + \frac{29}{2}e^{5} + \frac{463}{2}e^{4} - 52e^{3} - 271e^{2} - 18e + 23$ |
| 47 | $[47, 47, 8w - 83]$ | $-\frac{11}{4}e^{9} + \frac{3}{2}e^{8} + \frac{71}{2}e^{7} - 10e^{6} - \frac{581}{4}e^{5} - \frac{13}{4}e^{4} + \frac{377}{2}e^{3} + 72e^{2} - \frac{29}{2}e - 8$ |
| 47 | $[47, 47, -8w - 75]$ | $\phantom{-}\frac{3}{4}e^{9} - \frac{1}{2}e^{8} - \frac{19}{2}e^{7} + 4e^{6} + \frac{153}{4}e^{5} - \frac{23}{4}e^{4} - \frac{99}{2}e^{3} - 6e^{2} + \frac{7}{2}e - 1$ |
| 61 | $[61, 61, -1172w - 11031]$ | $\phantom{-}2e^{9} + \frac{3}{2}e^{8} - 28e^{7} - 24e^{6} + 125e^{5} + \frac{235}{2}e^{4} - \frac{353}{2}e^{3} - 177e^{2} + 5e + 15$ |
| 61 | $[61, 61, 1172w - 12203]$ | $\phantom{-}\frac{7}{4}e^{9} - 6e^{8} - \frac{35}{2}e^{7} + 69e^{6} + \frac{177}{4}e^{5} - \frac{957}{4}e^{4} - 9e^{3} + 239e^{2} + \frac{3}{2}e - 20$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,17w + 160]$ | $-1$ |
| $3$ | $[3,3,842w + 7925]$ | $-1$ |