Base field \(\Q(\sqrt{86}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 86\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} - 40x^{18} + 685x^{16} - 6562x^{14} + 38564x^{12} - 143500x^{10} + 336892x^{8} - 481248x^{6} + 384024x^{4} - 140096x^{2} + 11648\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -11w + 102]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 9]$ | $\phantom{-}\frac{421}{385024}e^{19} - \frac{3567}{96256}e^{17} + \frac{197617}{385024}e^{15} - \frac{713607}{192512}e^{13} + \frac{1406091}{96256}e^{11} - \frac{2769499}{96256}e^{9} + \frac{1453415}{96256}e^{7} + \frac{792859}{24064}e^{5} - \frac{2213289}{48128}e^{3} + \frac{162591}{12032}e$ |
| 5 | $[5, 5, w + 9]$ | $\phantom{-}\frac{421}{385024}e^{19} - \frac{3567}{96256}e^{17} + \frac{197617}{385024}e^{15} - \frac{713607}{192512}e^{13} + \frac{1406091}{96256}e^{11} - \frac{2769499}{96256}e^{9} + \frac{1453415}{96256}e^{7} + \frac{792859}{24064}e^{5} - \frac{2213289}{48128}e^{3} + \frac{162591}{12032}e$ |
| 7 | $[7, 7, 4w - 37]$ | $\phantom{-}\frac{239}{192512}e^{19} - \frac{2125}{48128}e^{17} + \frac{126419}{192512}e^{15} - \frac{507541}{96256}e^{13} + \frac{1182113}{48128}e^{11} - \frac{3183121}{48128}e^{9} + \frac{4642357}{48128}e^{7} - \frac{801711}{12032}e^{5} + \frac{500997}{24064}e^{3} - \frac{44451}{6016}e$ |
| 7 | $[7, 7, 4w + 37]$ | $\phantom{-}\frac{239}{192512}e^{19} - \frac{2125}{48128}e^{17} + \frac{126419}{192512}e^{15} - \frac{507541}{96256}e^{13} + \frac{1182113}{48128}e^{11} - \frac{3183121}{48128}e^{9} + \frac{4642357}{48128}e^{7} - \frac{801711}{12032}e^{5} + \frac{500997}{24064}e^{3} - \frac{44451}{6016}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{2423}{192512}e^{18} - \frac{22437}{48128}e^{16} + \frac{1401915}{192512}e^{14} - \frac{6000365}{96256}e^{12} + \frac{15300249}{48128}e^{10} - \frac{47274121}{48128}e^{8} + \frac{85864845}{48128}e^{6} - \frac{20957367}{12032}e^{4} + \frac{17681885}{24064}e^{2} - \frac{351371}{6016}$ |
| 11 | $[11, 11, 7w + 65]$ | $-\frac{127}{96256}e^{18} + \frac{1469}{24064}e^{16} - \frac{110371}{96256}e^{14} + \frac{551493}{48128}e^{12} - \frac{1600529}{24064}e^{10} + \frac{5492353}{24064}e^{8} - \frac{10783589}{24064}e^{6} + \frac{2752255}{6016}e^{4} - \frac{2355509}{12032}e^{2} + \frac{58483}{3008}$ |
| 11 | $[11, 11, -7w + 65]$ | $-\frac{127}{96256}e^{18} + \frac{1469}{24064}e^{16} - \frac{110371}{96256}e^{14} + \frac{551493}{48128}e^{12} - \frac{1600529}{24064}e^{10} + \frac{5492353}{24064}e^{8} - \frac{10783589}{24064}e^{6} + \frac{2752255}{6016}e^{4} - \frac{2355509}{12032}e^{2} + \frac{58483}{3008}$ |
| 17 | $[17, 17, -2w - 19]$ | $-\frac{1447}{192512}e^{18} + \frac{12853}{48128}e^{16} - \frac{770475}{192512}e^{14} + \frac{3168253}{96256}e^{12} - \frac{7787625}{48128}e^{10} + \frac{23353433}{48128}e^{8} - \frac{41720989}{48128}e^{6} + \frac{10280935}{12032}e^{4} - \frac{9230317}{24064}e^{2} + \frac{231291}{6016}$ |
| 17 | $[17, 17, 2w - 19]$ | $-\frac{1447}{192512}e^{18} + \frac{12853}{48128}e^{16} - \frac{770475}{192512}e^{14} + \frac{3168253}{96256}e^{12} - \frac{7787625}{48128}e^{10} + \frac{23353433}{48128}e^{8} - \frac{41720989}{48128}e^{6} + \frac{10280935}{12032}e^{4} - \frac{9230317}{24064}e^{2} + \frac{231291}{6016}$ |
| 29 | $[29, 29, -15w + 139]$ | $-\frac{3387}{385024}e^{19} + \frac{30769}{96256}e^{17} - \frac{1888111}{385024}e^{15} + \frac{7947033}{192512}e^{13} - \frac{19946389}{96256}e^{11} + \frac{60622021}{96256}e^{9} - \frac{107726393}{96256}e^{7} + \frac{25255803}{24064}e^{5} - \frac{19172681}{48128}e^{3} + \frac{184831}{12032}e$ |
| 29 | $[29, 29, -15w - 139]$ | $-\frac{3387}{385024}e^{19} + \frac{30769}{96256}e^{17} - \frac{1888111}{385024}e^{15} + \frac{7947033}{192512}e^{13} - \frac{19946389}{96256}e^{11} + \frac{60622021}{96256}e^{9} - \frac{107726393}{96256}e^{7} + \frac{25255803}{24064}e^{5} - \frac{19172681}{48128}e^{3} + \frac{184831}{12032}e$ |
| 37 | $[37, 37, -w - 7]$ | $\phantom{-}\frac{715}{385024}e^{19} - \frac{8673}{96256}e^{17} + \frac{669887}{385024}e^{15} - \frac{3396425}{192512}e^{13} + \frac{9898757}{96256}e^{11} - \frac{33796405}{96256}e^{9} + \frac{65506409}{96256}e^{7} - \frac{16450315}{24064}e^{5} + \frac{13780601}{48128}e^{3} - \frac{278095}{12032}e$ |
| 37 | $[37, 37, w - 7]$ | $\phantom{-}\frac{715}{385024}e^{19} - \frac{8673}{96256}e^{17} + \frac{669887}{385024}e^{15} - \frac{3396425}{192512}e^{13} + \frac{9898757}{96256}e^{11} - \frac{33796405}{96256}e^{9} + \frac{65506409}{96256}e^{7} - \frac{16450315}{24064}e^{5} + \frac{13780601}{48128}e^{3} - \frac{278095}{12032}e$ |
| 41 | $[41, 41, -40w + 371]$ | $\phantom{-}\frac{3737}{192512}e^{18} - \frac{34699}{48128}e^{16} + \frac{2175893}{192512}e^{14} - \frac{9347523}{96256}e^{12} + \frac{23892311}{48128}e^{10} - \frac{73745767}{48128}e^{8} + \frac{132979747}{48128}e^{6} - \frac{31935705}{12032}e^{4} + \frac{26232019}{24064}e^{2} - \frac{543301}{6016}$ |
| 41 | $[41, 41, 62w - 575]$ | $\phantom{-}\frac{3737}{192512}e^{18} - \frac{34699}{48128}e^{16} + \frac{2175893}{192512}e^{14} - \frac{9347523}{96256}e^{12} + \frac{23892311}{48128}e^{10} - \frac{73745767}{48128}e^{8} + \frac{132979747}{48128}e^{6} - \frac{31935705}{12032}e^{4} + \frac{26232019}{24064}e^{2} - \frac{543301}{6016}$ |
| 43 | $[43, 43, -51w + 473]$ | $-\frac{11}{752}e^{18} + \frac{49}{94}e^{16} - \frac{5927}{752}e^{14} + \frac{24783}{376}e^{12} - \frac{62507}{188}e^{10} + \frac{193837}{188}e^{8} - \frac{358329}{188}e^{6} + \frac{89764}{47}e^{4} - \frac{77381}{94}e^{2} + \frac{3018}{47}$ |
| 59 | $[59, 59, -5w + 47]$ | $\phantom{-}\frac{169}{48128}e^{18} - \frac{1339}{12032}e^{16} + \frac{71269}{48128}e^{14} - \frac{263539}{24064}e^{12} + \frac{608903}{12032}e^{10} - \frac{1865047}{12032}e^{8} + \frac{3753555}{12032}e^{6} - \frac{1101481}{3008}e^{4} + \frac{1156227}{6016}e^{2} - \frac{38933}{1504}$ |
| 59 | $[59, 59, 5w + 47]$ | $\phantom{-}\frac{169}{48128}e^{18} - \frac{1339}{12032}e^{16} + \frac{71269}{48128}e^{14} - \frac{263539}{24064}e^{12} + \frac{608903}{12032}e^{10} - \frac{1865047}{12032}e^{8} + \frac{3753555}{12032}e^{6} - \frac{1101481}{3008}e^{4} + \frac{1156227}{6016}e^{2} - \frac{38933}{1504}$ |
| 61 | $[61, 61, -w - 5]$ | $\phantom{-}\frac{1553}{96256}e^{19} - \frac{14387}{24064}e^{17} + \frac{900397}{96256}e^{15} - \frac{3866731}{48128}e^{13} + \frac{9918559}{24064}e^{11} - \frac{30960239}{24064}e^{9} + \frac{57255883}{24064}e^{7} - \frac{14475217}{6016}e^{5} + \frac{13310459}{12032}e^{3} - \frac{404829}{3008}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).