Base field \(\Q(\sqrt{101}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 25\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[17, 17, w + 6]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 2x^{8} - 18x^{7} - 17x^{6} + 117x^{5} + 4x^{4} - 258x^{3} + 118x^{2} + 91x - 29\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 5]$ | $\phantom{-}\frac{13}{127}e^{8} + \frac{87}{127}e^{7} + \frac{57}{127}e^{6} - \frac{569}{127}e^{5} - \frac{807}{127}e^{4} + \frac{808}{127}e^{3} + \frac{1385}{127}e^{2} - \frac{17}{127}e - \frac{157}{127}$ |
| 5 | $[5, 5, -w - 4]$ | $\phantom{-}\frac{321}{254}e^{8} + \frac{1269}{254}e^{7} - \frac{1636}{127}e^{6} - \frac{5838}{127}e^{5} + \frac{14715}{254}e^{4} + \frac{28519}{254}e^{3} - \frac{13786}{127}e^{2} - \frac{11967}{254}e + \frac{2746}{127}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{57}{127}e^{8} + \frac{421}{254}e^{7} - \frac{1327}{254}e^{6} - \frac{2065}{127}e^{5} + \frac{3134}{127}e^{4} + \frac{10749}{254}e^{3} - \frac{11037}{254}e^{2} - \frac{2722}{127}e + \frac{1427}{254}$ |
| 13 | $[13, 13, w + 3]$ | $-\frac{48}{127}e^{8} - \frac{204}{127}e^{7} + \frac{405}{127}e^{6} + \frac{1759}{127}e^{5} - \frac{1563}{127}e^{4} - \frac{4058}{127}e^{3} + \frac{2682}{127}e^{2} + \frac{1704}{127}e - \frac{153}{127}$ |
| 13 | $[13, 13, w - 4]$ | $-\frac{226}{127}e^{8} - \frac{897}{127}e^{7} + \frac{2272}{127}e^{6} + \frac{8192}{127}e^{5} - \frac{10042}{127}e^{4} - \frac{19625}{127}e^{3} + \frac{18438}{127}e^{2} + \frac{7515}{127}e - \frac{3435}{127}$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w + 7]$ | $-\frac{96}{127}e^{8} - \frac{408}{127}e^{7} + \frac{810}{127}e^{6} + \frac{3518}{127}e^{5} - \frac{3126}{127}e^{4} - \frac{7989}{127}e^{3} + \frac{5745}{127}e^{2} + \frac{3281}{127}e - \frac{1195}{127}$ |
| 19 | $[19, 19, w + 2]$ | $-\frac{57}{127}e^{8} - \frac{421}{254}e^{7} + \frac{1327}{254}e^{6} + \frac{2065}{127}e^{5} - \frac{3134}{127}e^{4} - \frac{10495}{254}e^{3} + \frac{11545}{254}e^{2} + \frac{1960}{127}e - \frac{2697}{254}$ |
| 19 | $[19, 19, w - 3]$ | $-\frac{137}{254}e^{8} - \frac{307}{127}e^{7} + \frac{1021}{254}e^{6} + \frac{2583}{127}e^{5} - \frac{3707}{254}e^{4} - \frac{5762}{127}e^{3} + \frac{7893}{254}e^{2} + \frac{4165}{254}e - \frac{2683}{254}$ |
| 23 | $[23, 23, w + 1]$ | $-\frac{51}{127}e^{8} - \frac{185}{127}e^{7} + \frac{597}{127}e^{6} + \frac{1734}{127}e^{5} - \frac{3018}{127}e^{4} - \frac{4137}{127}e^{3} + \frac{5977}{127}e^{2} + \frac{1239}{127}e - \frac{1377}{127}$ |
| 23 | $[23, 23, -w + 2]$ | $\phantom{-}e^{8} + 4e^{7} - 10e^{6} - 37e^{5} + 43e^{4} + 91e^{3} - 75e^{2} - 40e + 10$ |
| 31 | $[31, 31, -w - 7]$ | $-\frac{28}{127}e^{8} - \frac{119}{127}e^{7} + \frac{268}{127}e^{6} + \frac{1206}{127}e^{5} - \frac{880}{127}e^{4} - \frac{3362}{127}e^{3} + \frac{866}{127}e^{2} + \frac{2137}{127}e + \frac{6}{127}$ |
| 31 | $[31, 31, w - 8]$ | $\phantom{-}\frac{271}{254}e^{8} + \frac{993}{254}e^{7} - \frac{1560}{127}e^{6} - \frac{4734}{127}e^{5} + \frac{14849}{254}e^{4} + \frac{23477}{254}e^{3} - \frac{13167}{127}e^{2} - \frac{9049}{254}e + \frac{2071}{127}$ |
| 37 | $[37, 37, 2w - 9]$ | $-\frac{207}{254}e^{8} - \frac{424}{127}e^{7} + \frac{1945}{254}e^{6} + \frac{3773}{127}e^{5} - \frac{8447}{254}e^{4} - \frac{8885}{127}e^{3} + \frac{16789}{254}e^{2} + \frac{6269}{254}e - \frac{5335}{254}$ |
| 37 | $[37, 37, 2w + 7]$ | $-\frac{222}{127}e^{8} - \frac{880}{127}e^{7} + \frac{2270}{127}e^{6} + \frac{8183}{127}e^{5} - \frac{10134}{127}e^{4} - \frac{20451}{127}e^{3} + \frac{18532}{127}e^{2} + \frac{9405}{127}e - \frac{3200}{127}$ |
| 43 | $[43, 43, 4w + 17]$ | $-\frac{63}{127}e^{8} - \frac{236}{127}e^{7} + \frac{730}{127}e^{6} + \frac{2396}{127}e^{5} - \frac{3250}{127}e^{4} - \frac{6485}{127}e^{3} + \frac{5314}{127}e^{2} + \frac{3443}{127}e - \frac{685}{127}$ |
| 43 | $[43, 43, 4w - 21]$ | $\phantom{-}\frac{213}{127}e^{8} + \frac{810}{127}e^{7} - \frac{2329}{127}e^{6} - \frac{7623}{127}e^{5} + \frac{10849}{127}e^{4} + \frac{18817}{127}e^{3} - \frac{19950}{127}e^{2} - \frac{7879}{127}e + \frac{3465}{127}$ |
| 47 | $[47, 47, -w - 8]$ | $-\frac{162}{127}e^{8} - \frac{625}{127}e^{7} + \frac{1732}{127}e^{6} + \frac{5889}{127}e^{5} - \frac{7831}{127}e^{4} - \frac{14807}{127}e^{3} + \frac{13592}{127}e^{2} + \frac{7021}{127}e - \frac{1834}{127}$ |
| 47 | $[47, 47, w - 9]$ | $-\frac{340}{127}e^{8} - \frac{1445}{127}e^{7} + \frac{2964}{127}e^{6} + \frac{12830}{127}e^{5} - \frac{11738}{127}e^{4} - \frac{30755}{127}e^{3} + \frac{21728}{127}e^{2} + \frac{13975}{127}e - \frac{4100}{127}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w + 6]$ | $-1$ |