Base field \(\Q(\sqrt{193}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 48\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6, 6, -251w - 1618]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 16x^{7} - 4x^{6} + 85x^{5} + 37x^{4} - 164x^{3} - 82x^{2} + 94x + 45\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -9w - 58]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -9w + 67]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -2w + 15]$ | $-\frac{5}{26}e^{8} + \frac{2}{13}e^{7} + \frac{69}{26}e^{6} - \frac{15}{13}e^{5} - \frac{155}{13}e^{4} + \frac{37}{26}e^{3} + 18e^{2} + \frac{7}{26}e - \frac{74}{13}$ |
| 3 | $[3, 3, 2w + 13]$ | $\phantom{-}1$ |
| 7 | $[7, 7, 186w - 1385]$ | $-\frac{1}{13}e^{8} - \frac{1}{26}e^{7} + \frac{19}{13}e^{6} + \frac{1}{26}e^{5} - \frac{114}{13}e^{4} + \frac{23}{13}e^{3} + \frac{37}{2}e^{2} - \frac{48}{13}e - \frac{223}{26}$ |
| 7 | $[7, 7, -186w - 1199]$ | $-\frac{3}{13}e^{8} + \frac{5}{13}e^{7} + \frac{44}{13}e^{6} - \frac{57}{13}e^{5} - \frac{212}{13}e^{4} + \frac{186}{13}e^{3} + 28e^{2} - \frac{170}{13}e - \frac{185}{13}$ |
| 23 | $[23, 23, -38w - 245]$ | $\phantom{-}\frac{5}{26}e^{8} - \frac{2}{13}e^{7} - \frac{69}{26}e^{6} + \frac{28}{13}e^{5} + \frac{142}{13}e^{4} - \frac{245}{26}e^{3} - 12e^{2} + \frac{279}{26}e + \frac{9}{13}$ |
| 23 | $[23, 23, 38w - 283]$ | $-\frac{3}{13}e^{8} - \frac{3}{26}e^{7} + \frac{44}{13}e^{6} + \frac{55}{26}e^{5} - \frac{199}{13}e^{4} - \frac{139}{13}e^{3} + \frac{43}{2}e^{2} + \frac{168}{13}e - \frac{201}{26}$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{4}{13}e^{8} - \frac{9}{26}e^{7} - \frac{50}{13}e^{6} + \frac{87}{26}e^{5} + \frac{183}{13}e^{4} - \frac{118}{13}e^{3} - \frac{23}{2}e^{2} + \frac{88}{13}e - \frac{109}{26}$ |
| 31 | $[31, 31, 16w - 119]$ | $\phantom{-}\frac{1}{13}e^{8} + \frac{1}{26}e^{7} - \frac{19}{13}e^{6} - \frac{27}{26}e^{5} + \frac{101}{13}e^{4} + \frac{81}{13}e^{3} - \frac{17}{2}e^{2} - \frac{69}{13}e - \frac{115}{26}$ |
| 31 | $[31, 31, 16w + 103]$ | $-\frac{1}{13}e^{8} + \frac{6}{13}e^{7} + \frac{6}{13}e^{6} - \frac{71}{13}e^{5} + \frac{16}{13}e^{4} + \frac{231}{13}e^{3} - 8e^{2} - \frac{152}{13}e + \frac{103}{13}$ |
| 43 | $[43, 43, 4w + 25]$ | $\phantom{-}\frac{1}{13}e^{8} - \frac{6}{13}e^{7} - \frac{6}{13}e^{6} + \frac{71}{13}e^{5} - \frac{16}{13}e^{4} - \frac{257}{13}e^{3} + 8e^{2} + \frac{282}{13}e - \frac{77}{13}$ |
| 43 | $[43, 43, -4w + 29]$ | $-\frac{1}{13}e^{8} + \frac{6}{13}e^{7} + \frac{6}{13}e^{6} - \frac{58}{13}e^{5} - \frac{10}{13}e^{4} + \frac{140}{13}e^{3} + 3e^{2} - \frac{22}{13}e - \frac{14}{13}$ |
| 59 | $[59, 59, 12w - 89]$ | $\phantom{-}\frac{1}{2}e^{8} - e^{7} - \frac{13}{2}e^{6} + 11e^{5} + 28e^{4} - \frac{73}{2}e^{3} - 43e^{2} + \frac{79}{2}e + 18$ |
| 59 | $[59, 59, -12w - 77]$ | $-\frac{3}{13}e^{8} + \frac{5}{13}e^{7} + \frac{31}{13}e^{6} - \frac{44}{13}e^{5} - \frac{82}{13}e^{4} + \frac{108}{13}e^{3} + 2e^{2} - \frac{105}{13}e - \frac{42}{13}$ |
| 67 | $[67, 67, 92w + 593]$ | $-\frac{3}{13}e^{8} + \frac{5}{13}e^{7} + \frac{44}{13}e^{6} - \frac{70}{13}e^{5} - \frac{212}{13}e^{4} + \frac{303}{13}e^{3} + 29e^{2} - \frac{378}{13}e - \frac{172}{13}$ |
| 67 | $[67, 67, 92w - 685]$ | $\phantom{-}\frac{4}{13}e^{8} - \frac{11}{13}e^{7} - \frac{50}{13}e^{6} + \frac{128}{13}e^{5} + \frac{222}{13}e^{4} - \frac{443}{13}e^{3} - 34e^{2} + \frac{374}{13}e + \frac{290}{13}$ |
| 83 | $[83, 83, 204w - 1519]$ | $\phantom{-}\frac{5}{13}e^{8} + \frac{5}{26}e^{7} - \frac{69}{13}e^{6} - \frac{83}{26}e^{5} + \frac{271}{13}e^{4} + \frac{197}{13}e^{3} - \frac{37}{2}e^{2} - \frac{215}{13}e - \frac{159}{26}$ |
| 83 | $[83, 83, 204w + 1315]$ | $\phantom{-}\frac{6}{13}e^{8} - \frac{10}{13}e^{7} - \frac{75}{13}e^{6} + \frac{88}{13}e^{5} + \frac{281}{13}e^{4} - \frac{164}{13}e^{3} - 20e^{2} + \frac{2}{13}e + \frac{6}{13}$ |
| 97 | $[97, 97, -24w + 179]$ | $\phantom{-}\frac{5}{13}e^{8} - \frac{4}{13}e^{7} - \frac{82}{13}e^{6} + \frac{43}{13}e^{5} + \frac{414}{13}e^{4} - \frac{115}{13}e^{3} - 48e^{2} + \frac{84}{13}e + \frac{109}{13}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -9w - 58]$ | $-1$ |
| $3$ | $[3, 3, 2w + 13]$ | $-1$ |