Base field 4.4.15188.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 28x^{14} + 317x^{12} - 1861x^{10} + 6043x^{8} - 10716x^{6} + 9516x^{4} - 3356x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{545}{98144}e^{15} - \frac{3159}{24536}e^{13} + \frac{112557}{98144}e^{11} - \frac{485285}{98144}e^{9} + \frac{1067243}{98144}e^{7} - \frac{317283}{24536}e^{5} + \frac{278095}{24536}e^{3} - \frac{180343}{24536}e$ |
| 2 | $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ | $-1$ |
| 11 | $[11, 11, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{659}{12268}e^{15} + \frac{4028}{3067}e^{13} - \frac{154987}{12268}e^{11} + \frac{744815}{12268}e^{9} - \frac{1871941}{12268}e^{7} + \frac{582831}{3067}e^{5} - \frac{295100}{3067}e^{3} + \frac{25965}{3067}e$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $\phantom{-}\frac{127}{24536}e^{15} - \frac{995}{6134}e^{13} + \frac{51035}{24536}e^{11} - \frac{343363}{24536}e^{9} + \frac{1285917}{24536}e^{7} - \frac{650149}{6134}e^{5} + \frac{619565}{6134}e^{3} - \frac{173889}{6134}e$ |
| 19 | $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ | $-\frac{1177}{24536}e^{15} + \frac{7869}{6134}e^{13} - \frac{332717}{24536}e^{11} + \frac{1756205}{24536}e^{9} - \frac{4804779}{24536}e^{7} + \frac{1598967}{6134}e^{5} - \frac{865133}{6134}e^{3} + \frac{124711}{6134}e$ |
| 23 | $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ | $\phantom{-}\frac{77}{6134}e^{14} - \frac{313}{3067}e^{12} - \frac{7069}{6134}e^{10} + \frac{97505}{6134}e^{8} - \frac{387983}{6134}e^{6} + \frac{309399}{3067}e^{4} - \frac{187629}{3067}e^{2} + \frac{45080}{3067}$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 6w - 1]$ | $-\frac{3847}{49072}e^{15} + \frac{22895}{12268}e^{13} - \frac{850603}{49072}e^{11} + \frac{3892123}{49072}e^{9} - \frac{9057253}{49072}e^{7} + \frac{2444351}{12268}e^{5} - \frac{916837}{12268}e^{3} + \frac{88689}{12268}e$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $-\frac{31}{49072}e^{15} - \frac{1351}{12268}e^{13} + \frac{112541}{49072}e^{11} - \frac{798517}{49072}e^{9} + \frac{2394155}{49072}e^{7} - \frac{713103}{12268}e^{5} + \frac{253515}{12268}e^{3} - \frac{58983}{12268}e$ |
| 43 | $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ | $\phantom{-}\frac{3053}{49072}e^{15} - \frac{22277}{12268}e^{13} + \frac{1021481}{49072}e^{11} - \frac{5826905}{49072}e^{9} + \frac{17298439}{49072}e^{7} - \frac{6386297}{12268}e^{5} + \frac{4056575}{12268}e^{3} - \frac{758859}{12268}e$ |
| 67 | $[67, 67, w^{2} - w - 5]$ | $-\frac{293}{3067}e^{14} + \frac{6405}{3067}e^{12} - \frac{54277}{3067}e^{10} + \frac{229748}{3067}e^{8} - \frac{525245}{3067}e^{6} + \frac{633806}{3067}e^{4} - \frac{324084}{3067}e^{2} + \frac{30540}{3067}$ |
| 67 | $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ | $-\frac{2293}{24536}e^{15} + \frac{14439}{6134}e^{13} - \frac{575041}{24536}e^{11} + \frac{2869905}{24536}e^{9} - \frac{7484591}{24536}e^{7} + \frac{2395469}{6134}e^{5} - \frac{1234025}{6134}e^{3} + \frac{160491}{6134}e$ |
| 73 | $[73, 73, w^{2} + w + 1]$ | $-\frac{511}{6134}e^{14} + \frac{5423}{3067}e^{12} - \frac{85805}{6134}e^{10} + \frac{310383}{6134}e^{8} - \frac{493319}{6134}e^{6} + \frac{103932}{3067}e^{4} + \frac{84733}{3067}e^{2} - \frac{22022}{3067}$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ | $\phantom{-}\frac{1661}{6134}e^{14} - \frac{19458}{3067}e^{12} + \frac{354881}{6134}e^{10} - \frac{1592851}{6134}e^{8} + \frac{3655045}{6134}e^{6} - \frac{1997545}{3067}e^{4} + \frac{843125}{3067}e^{2} - \frac{94876}{3067}$ |
| 81 | $[81, 3, -3]$ | $-\frac{173}{3067}e^{14} + \frac{3876}{3067}e^{12} - \frac{33827}{3067}e^{10} + \frac{148811}{3067}e^{8} - \frac{363104}{3067}e^{6} + \frac{506673}{3067}e^{4} - \frac{350628}{3067}e^{2} + \frac{50042}{3067}$ |
| 83 | $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ | $\phantom{-}\frac{3979}{49072}e^{15} - \frac{22287}{12268}e^{13} + \frac{771887}{49072}e^{11} - \frac{3293839}{49072}e^{9} + \frac{7428225}{49072}e^{7} - \frac{2286935}{12268}e^{5} + \frac{1666473}{12268}e^{3} - \frac{651181}{12268}e$ |
| 83 | $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ | $\phantom{-}\frac{275}{6134}e^{14} - \frac{1556}{3067}e^{12} - \frac{8597}{6134}e^{10} + \frac{234315}{6134}e^{8} - \frac{1040397}{6134}e^{6} + \frac{861389}{3067}e^{4} - \frac{490465}{3067}e^{2} + \frac{62856}{3067}$ |
| 89 | $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ | $-\frac{61}{24536}e^{15} + \frac{1299}{6134}e^{13} - \frac{90393}{24536}e^{11} + \frac{642505}{24536}e^{9} - \frac{2100431}{24536}e^{7} + \frac{728857}{6134}e^{5} - \frac{244747}{6134}e^{3} - \frac{131893}{6134}e$ |
| 89 | $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ | $-\frac{13}{49072}e^{15} + \frac{3193}{12268}e^{13} - \frac{266233}{49072}e^{11} + \frac{2095785}{49072}e^{9} - \frac{7682535}{49072}e^{7} + \frac{3304385}{12268}e^{5} - \frac{2323147}{12268}e^{3} + \frac{401875}{12268}e$ |
| 97 | $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ | $\phantom{-}\frac{1113}{6134}e^{14} - \frac{12610}{3067}e^{12} + \frac{219577}{6134}e^{10} - \frac{919299}{6134}e^{8} + \frac{1864767}{6134}e^{6} - \frac{752552}{3067}e^{4} + \frac{37613}{3067}e^{2} + \frac{48806}{3067}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ | $1$ |