Base field 3.3.788.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[17, 17, w^{2} - 2w - 8]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 32x^{14} + 410x^{12} - 2690x^{10} + 9612x^{8} - 18496x^{6} + 18072x^{4} - 7848x^{2} + 1152\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $-\frac{241}{50928}e^{14} + \frac{1799}{12732}e^{12} - \frac{21029}{12732}e^{10} + \frac{243103}{25464}e^{8} - \frac{119815}{4244}e^{6} + \frac{499483}{12732}e^{4} - \frac{40629}{2122}e^{2} + \frac{1295}{1061}$ |
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + 2w + 4]$ | $-\frac{73}{8488}e^{15} + \frac{7063}{25464}e^{13} - \frac{90653}{25464}e^{11} + \frac{73519}{3183}e^{9} - \frac{1011553}{12732}e^{7} + \frac{590545}{4244}e^{5} - \frac{700789}{6366}e^{3} + \frac{61759}{2122}e$ |
| 9 | $[9, 3, w^{2} - w - 7]$ | $\phantom{-}\frac{79}{25464}e^{15} - \frac{377}{4244}e^{13} + \frac{24223}{25464}e^{11} - \frac{28735}{6366}e^{9} + \frac{47501}{6366}e^{7} + \frac{102745}{12732}e^{5} - \frac{102325}{3183}e^{3} + \frac{38281}{2122}e$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{45}{8488}e^{15} - \frac{1879}{12732}e^{13} + \frac{9781}{6366}e^{11} - \frac{91211}{12732}e^{9} + \frac{40499}{3183}e^{7} + \frac{8345}{2122}e^{5} - \frac{84419}{3183}e^{3} + \frac{10273}{1061}e$ |
| 13 | $[13, 13, w - 2]$ | $\phantom{-}\frac{163}{16976}e^{15} - \frac{1955}{6366}e^{13} + \frac{99835}{25464}e^{11} - \frac{649441}{25464}e^{9} + \frac{1139387}{12732}e^{7} - \frac{350165}{2122}e^{5} + \frac{907811}{6366}e^{3} - \frac{79829}{2122}e$ |
| 17 | $[17, 17, w^{2} - 2w - 8]$ | $\phantom{-}1$ |
| 25 | $[25, 5, -w^{2} + 2]$ | $\phantom{-}\frac{823}{50928}e^{15} - \frac{1592}{3183}e^{13} + \frac{156265}{25464}e^{11} - \frac{965611}{25464}e^{9} + \frac{524867}{4244}e^{7} - \frac{1291967}{6366}e^{5} + \frac{302659}{2122}e^{3} - \frac{51835}{2122}e$ |
| 31 | $[31, 31, 3w^{2} - 5w - 19]$ | $\phantom{-}\frac{303}{8488}e^{14} - \frac{9307}{8488}e^{12} + \frac{56237}{4244}e^{10} - \frac{337791}{4244}e^{8} + \frac{1047323}{4244}e^{6} - \frac{791903}{2122}e^{4} + \frac{516843}{2122}e^{2} - \frac{54824}{1061}$ |
| 53 | $[53, 53, 2w^{2} - 3w - 10]$ | $\phantom{-}\frac{161}{8488}e^{15} - \frac{15025}{25464}e^{13} + \frac{184091}{25464}e^{11} - \frac{140227}{3183}e^{9} + \frac{1758451}{12732}e^{7} - \frac{871727}{4244}e^{5} + \frac{697735}{6366}e^{3} + \frac{3931}{2122}e$ |
| 53 | $[53, 53, w^{2} - 3w - 5]$ | $\phantom{-}\frac{215}{4244}e^{14} - \frac{6653}{4244}e^{12} + \frac{20332}{1061}e^{10} - \frac{248847}{2122}e^{8} + \frac{796235}{2122}e^{6} - \frac{635397}{1061}e^{4} + \frac{447835}{1061}e^{2} - \frac{98946}{1061}$ |
| 53 | $[53, 53, 2w - 1]$ | $\phantom{-}\frac{445}{50928}e^{15} - \frac{3313}{12732}e^{13} + \frac{25201}{8488}e^{11} - \frac{135167}{8488}e^{9} + \frac{488821}{12732}e^{7} - \frac{171587}{6366}e^{5} - \frac{100415}{6366}e^{3} + \frac{28047}{2122}e$ |
| 59 | $[59, 59, 2w^{2} - 4w - 11]$ | $-\frac{313}{8488}e^{14} + \frac{9271}{8488}e^{12} - \frac{53835}{4244}e^{10} + \frac{310281}{4244}e^{8} - \frac{924615}{4244}e^{6} + \frac{670745}{2122}e^{4} - \frac{392735}{2122}e^{2} + \frac{32500}{1061}$ |
| 59 | $[59, 59, 2w^{2} - 6w - 5]$ | $-\frac{65}{8488}e^{14} + \frac{236}{1061}e^{12} - \frac{2728}{1061}e^{10} + \frac{65215}{4244}e^{8} - \frac{110479}{2122}e^{6} + \frac{216179}{2122}e^{4} - \frac{108051}{1061}e^{2} + \frac{31020}{1061}$ |
| 59 | $[59, 59, 2w + 5]$ | $\phantom{-}\frac{25}{3183}e^{14} - \frac{971}{3183}e^{12} + \frac{30091}{6366}e^{10} - \frac{118151}{3183}e^{8} + \frac{164361}{1061}e^{6} - \frac{1044106}{3183}e^{4} + \frac{319104}{1061}e^{2} - \frac{81764}{1061}$ |
| 67 | $[67, 67, w^{2} - 3w - 7]$ | $\phantom{-}\frac{101}{12732}e^{14} - \frac{2395}{12732}e^{12} + \frac{8843}{6366}e^{10} - \frac{6497}{6366}e^{8} - \frac{63765}{2122}e^{6} + \frac{393145}{3183}e^{4} - \frac{165383}{1061}e^{2} + \frac{52420}{1061}$ |
| 71 | $[71, 71, 2w^{2} - 2w - 13]$ | $-\frac{593}{8488}e^{15} + \frac{27779}{12732}e^{13} - \frac{343819}{12732}e^{11} + \frac{2142523}{12732}e^{9} - \frac{1764046}{3183}e^{7} + \frac{984501}{1061}e^{5} - \frac{2229035}{3183}e^{3} + \frac{177714}{1061}e$ |
| 73 | $[73, 73, 2w^{2} - 4w - 7]$ | $\phantom{-}\frac{25}{1061}e^{15} - \frac{4765}{6366}e^{13} + \frac{241199}{25464}e^{11} - \frac{773785}{12732}e^{9} + \frac{1323497}{6366}e^{7} - \frac{1548327}{4244}e^{5} + \frac{925001}{3183}e^{3} - \frac{162735}{2122}e$ |
| 79 | $[79, 79, -w^{2} + 10]$ | $\phantom{-}\frac{171}{8488}e^{15} - \frac{2663}{4244}e^{13} + \frac{32347}{4244}e^{11} - \frac{191643}{4244}e^{9} + \frac{140352}{1061}e^{7} - \frac{178838}{1061}e^{5} + \frac{65022}{1061}e^{3} + \frac{12088}{1061}e$ |
| 89 | $[89, 89, 2w^{2} - w - 10]$ | $-\frac{2027}{50928}e^{15} + \frac{7735}{6366}e^{13} - \frac{123609}{8488}e^{11} + \frac{734325}{8488}e^{9} - \frac{3364805}{12732}e^{7} + \frac{1244507}{3183}e^{5} - \frac{1552901}{6366}e^{3} + \frac{102169}{2122}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{2} - 2w - 8]$ | $-1$ |