Base field \(\Q(\sqrt{113}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11,11,-4w + 23]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 2x^{15} - 21x^{14} + 38x^{13} + 178x^{12} - 280x^{11} - 781x^{10} + 1012x^{9} + 1884x^{8} - 1880x^{7} - 2438x^{6} + 1731x^{5} + 1543x^{4} - 679x^{3} - 368x^{2} + 65x + 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 6]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 5]$ | $-\frac{25}{6212}e^{15} - \frac{45}{12424}e^{14} + \frac{3249}{12424}e^{13} - \frac{2883}{12424}e^{12} - \frac{22685}{6212}e^{11} + \frac{50151}{12424}e^{10} + \frac{260119}{12424}e^{9} - \frac{277285}{12424}e^{8} - \frac{86181}{1553}e^{7} + \frac{628165}{12424}e^{6} + \frac{816877}{12424}e^{5} - \frac{144597}{3106}e^{4} - \frac{47237}{1553}e^{3} + \frac{211201}{12424}e^{2} + \frac{14703}{6212}e - \frac{21713}{12424}$ |
| 7 | $[7, 7, 6w - 35]$ | $-\frac{1715}{6212}e^{15} + \frac{5445}{6212}e^{14} + \frac{29287}{6212}e^{13} - \frac{49987}{3106}e^{12} - \frac{183339}{6212}e^{11} + \frac{705915}{6212}e^{10} + \frac{498765}{6212}e^{9} - \frac{602834}{1553}e^{8} - \frac{477617}{6212}e^{7} + \frac{4108199}{6212}e^{6} - \frac{98555}{3106}e^{5} - \frac{1597759}{3106}e^{4} + \frac{441489}{6212}e^{3} + \frac{440699}{3106}e^{2} - \frac{90277}{6212}e - \frac{18061}{3106}$ |
| 7 | $[7, 7, -6w - 29]$ | $-\frac{187}{3106}e^{15} - \frac{13}{3106}e^{14} + \frac{5287}{3106}e^{13} - \frac{1247}{3106}e^{12} - \frac{55383}{3106}e^{11} + \frac{20493}{3106}e^{10} + \frac{275517}{3106}e^{9} - \frac{109439}{3106}e^{8} - \frac{679465}{3106}e^{7} + \frac{234617}{3106}e^{6} + \frac{392581}{1553}e^{5} - \frac{187693}{3106}e^{4} - \frac{368659}{3106}e^{3} + \frac{37339}{3106}e^{2} + \frac{21227}{1553}e + \frac{1941}{3106}$ |
| 9 | $[9, 3, 3]$ | $-\frac{515}{1553}e^{15} + \frac{5911}{6212}e^{14} + \frac{36641}{6212}e^{13} - \frac{109151}{6212}e^{12} - \frac{60425}{1553}e^{11} + \frac{771951}{6212}e^{10} + \frac{702227}{6212}e^{9} - \frac{2613973}{6212}e^{8} - \frac{361361}{3106}e^{7} + \frac{4310781}{6212}e^{6} - \frac{355057}{6212}e^{5} - \frac{1539821}{3106}e^{4} + \frac{415493}{3106}e^{3} + \frac{688933}{6212}e^{2} - \frac{96503}{3106}e - \frac{24585}{6212}$ |
| 11 | $[11, 11, 4w + 19]$ | $\phantom{-}\frac{1815}{6212}e^{15} - \frac{12263}{12424}e^{14} - \frac{63805}{12424}e^{13} + \frac{228563}{12424}e^{12} + \frac{211959}{6212}e^{11} - \frac{1638835}{12424}e^{10} - \frac{1325179}{12424}e^{9} + \frac{5672461}{12424}e^{8} + \frac{491087}{3106}e^{7} - \frac{9721161}{12424}e^{6} - \frac{1178965}{12424}e^{5} + \frac{1868653}{3106}e^{4} + \frac{50771}{3106}e^{3} - \frac{1888561}{12424}e^{2} - \frac{15125}{6212}e + \frac{36409}{12424}$ |
| 11 | $[11, 11, 4w - 23]$ | $-1$ |
| 13 | $[13, 13, -2w + 11]$ | $\phantom{-}\frac{773}{6212}e^{15} - \frac{2255}{6212}e^{14} - \frac{14231}{6212}e^{13} + \frac{10343}{1553}e^{12} + \frac{101341}{6212}e^{11} - \frac{289525}{6212}e^{10} - \frac{352353}{6212}e^{9} + \frac{483489}{3106}e^{8} + \frac{619715}{6212}e^{7} - \frac{1585669}{6212}e^{6} - \frac{129990}{1553}e^{5} + \frac{299593}{1553}e^{4} + \frac{227059}{6212}e^{3} - \frac{175233}{3106}e^{2} - \frac{63385}{6212}e + \frac{6791}{1553}$ |
| 13 | $[13, 13, 2w + 9]$ | $-\frac{1875}{6212}e^{15} + \frac{12155}{12424}e^{14} + \frac{66633}{12424}e^{13} - \frac{231755}{12424}e^{12} - \frac{216707}{6212}e^{11} + \frac{1702047}{12424}e^{10} + \frac{1186631}{12424}e^{9} - \frac{6021133}{12424}e^{8} - \frac{209633}{3106}e^{7} + \frac{10446045}{12424}e^{6} - \frac{1646255}{12424}e^{5} - \frac{998667}{1553}e^{4} + \frac{541233}{3106}e^{3} + \frac{2058753}{12424}e^{2} - \frac{186265}{6212}e - \frac{97217}{12424}$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{2085}{6212}e^{15} - \frac{1278}{1553}e^{14} - \frac{19521}{3106}e^{13} + \frac{89627}{6212}e^{12} + \frac{289233}{6212}e^{11} - \frac{295627}{3106}e^{10} - \frac{546207}{3106}e^{9} + \frac{1826251}{6212}e^{8} + \frac{2246173}{6212}e^{7} - \frac{673427}{1553}e^{6} - \frac{2406953}{6212}e^{5} + \frac{432217}{1553}e^{4} + \frac{1145465}{6212}e^{3} - \frac{312327}{6212}e^{2} - \frac{157145}{6212}e - \frac{15031}{6212}$ |
| 31 | $[31, 31, 2w - 13]$ | $\phantom{-}\frac{501}{3106}e^{15} - \frac{784}{1553}e^{14} - \frac{8235}{3106}e^{13} + \frac{14273}{1553}e^{12} + \frac{46479}{3106}e^{11} - \frac{99575}{1553}e^{10} - \frac{85159}{3106}e^{9} + \frac{334012}{1553}e^{8} - \frac{110235}{3106}e^{7} - \frac{551966}{1553}e^{6} + \frac{280834}{1553}e^{5} + \frac{805783}{3106}e^{4} - \frac{289203}{1553}e^{3} - \frac{182221}{3106}e^{2} + \frac{160443}{3106}e + \frac{1299}{1553}$ |
| 31 | $[31, 31, -2w - 11]$ | $\phantom{-}\frac{693}{6212}e^{15} - \frac{970}{1553}e^{14} - \frac{4361}{3106}e^{13} + \frac{71857}{6212}e^{12} + \frac{22537}{6212}e^{11} - \frac{256991}{3106}e^{10} + \frac{55369}{3106}e^{9} + \frac{1789017}{6212}e^{8} - \frac{645535}{6212}e^{7} - \frac{781493}{1553}e^{6} + \frac{1024031}{6212}e^{5} + \frac{1251219}{3106}e^{4} - \frac{450255}{6212}e^{3} - \frac{724129}{6212}e^{2} - \frac{80319}{6212}e + \frac{55475}{6212}$ |
| 41 | $[41, 41, -8w - 39]$ | $\phantom{-}\frac{3005}{6212}e^{15} - \frac{19439}{12424}e^{14} - \frac{96081}{12424}e^{13} + \frac{341567}{12424}e^{12} + \frac{266785}{6212}e^{11} - \frac{2266163}{12424}e^{10} - \frac{1079711}{12424}e^{9} + \frac{7065321}{12424}e^{8} - \frac{23470}{1553}e^{7} - \frac{10453369}{12424}e^{6} + \frac{3030955}{12424}e^{5} + \frac{1572883}{3106}e^{4} - \frac{649847}{3106}e^{3} - \frac{770689}{12424}e^{2} + \frac{154071}{6212}e - \frac{66227}{12424}$ |
| 41 | $[41, 41, 8w - 47]$ | $-\frac{2039}{6212}e^{15} + \frac{1366}{1553}e^{14} + \frac{19859}{3106}e^{13} - \frac{108903}{6212}e^{12} - \frac{292219}{6212}e^{11} + \frac{419813}{3106}e^{10} + \frac{489573}{3106}e^{9} - \frac{3126323}{6212}e^{8} - \frac{1327247}{6212}e^{7} + \frac{1425263}{1553}e^{6} + \frac{68695}{6212}e^{5} - \frac{2271205}{3106}e^{4} + \frac{867885}{6212}e^{3} + \frac{1173503}{6212}e^{2} - \frac{258407}{6212}e - \frac{32269}{6212}$ |
| 53 | $[53, 53, -26w - 125]$ | $-\frac{631}{3106}e^{15} + \frac{7357}{12424}e^{14} + \frac{41571}{12424}e^{13} - \frac{126463}{12424}e^{12} - \frac{61943}{3106}e^{11} + \frac{815309}{12424}e^{10} + \frac{625989}{12424}e^{9} - \frac{2451413}{12424}e^{8} - \frac{242819}{6212}e^{7} + \frac{3480267}{12424}e^{6} - \frac{566647}{12424}e^{5} - \frac{502521}{3106}e^{4} + \frac{594733}{6212}e^{3} + \frac{211041}{12424}e^{2} - \frac{71656}{1553}e + \frac{33083}{12424}$ |
| 53 | $[53, 53, 26w - 151]$ | $\phantom{-}\frac{2993}{3106}e^{15} - \frac{9575}{3106}e^{14} - \frac{26286}{1553}e^{13} + \frac{89037}{1553}e^{12} + \frac{342243}{3106}e^{11} - \frac{1269481}{3106}e^{10} - \frac{491868}{1553}e^{9} + \frac{2168129}{1553}e^{8} + \frac{1024735}{3106}e^{7} - \frac{7224811}{3106}e^{6} + \frac{381135}{3106}e^{5} + \frac{2630209}{1553}e^{4} - \frac{468705}{1553}e^{3} - \frac{1236297}{3106}e^{2} + \frac{70097}{1553}e + \frac{23188}{1553}$ |
| 61 | $[61, 61, -14w + 81]$ | $-\frac{4535}{6212}e^{15} + \frac{6889}{3106}e^{14} + \frac{39331}{3106}e^{13} - \frac{247977}{6212}e^{12} - \frac{505887}{6212}e^{11} + \frac{423221}{1553}e^{10} + \frac{720323}{3106}e^{9} - \frac{5456933}{6212}e^{8} - \frac{1487299}{6212}e^{7} + \frac{4204963}{3106}e^{6} - \frac{663377}{6212}e^{5} - \frac{2742945}{3106}e^{4} + \frac{1669639}{6212}e^{3} + \frac{999963}{6212}e^{2} - \frac{402225}{6212}e + \frac{11793}{6212}$ |
| 61 | $[61, 61, -14w - 67]$ | $\phantom{-}\frac{3063}{6212}e^{15} - \frac{11065}{6212}e^{14} - \frac{49045}{6212}e^{13} + \frac{103945}{3106}e^{12} + \frac{259779}{6212}e^{11} - \frac{1507727}{6212}e^{10} - \frac{358331}{6212}e^{9} + \frac{1322049}{1553}e^{8} - \frac{1104235}{6212}e^{7} - \frac{9112139}{6212}e^{6} + \frac{918840}{1553}e^{5} + \frac{3374877}{3106}e^{4} - \frac{3001555}{6212}e^{3} - \frac{370260}{1553}e^{2} + \frac{508707}{6212}e + \frac{23323}{3106}$ |
| 83 | $[83, 83, 2w - 15]$ | $\phantom{-}\frac{5731}{6212}e^{15} - \frac{15497}{6212}e^{14} - \frac{103017}{6212}e^{13} + \frac{138187}{3106}e^{12} + \frac{707791}{6212}e^{11} - \frac{1868075}{6212}e^{10} - \frac{2324783}{6212}e^{9} + \frac{1492149}{1553}e^{8} + \frac{3683965}{6212}e^{7} - \frac{9175055}{6212}e^{6} - \frac{582556}{1553}e^{5} + \frac{3035119}{3106}e^{4} + \frac{211173}{6212}e^{3} - \frac{290125}{1553}e^{2} + \frac{43351}{6212}e - \frac{6585}{3106}$ |
| 83 | $[83, 83, -2w - 13]$ | $\phantom{-}\frac{4993}{6212}e^{15} - \frac{26421}{12424}e^{14} - \frac{183363}{12424}e^{13} + \frac{476525}{12424}e^{12} + \frac{650633}{6212}e^{11} - \frac{3269553}{12424}e^{10} - \frac{4509053}{12424}e^{9} + \frac{10664763}{12424}e^{8} + \frac{1979049}{3106}e^{7} - \frac{16915459}{12424}e^{6} - \frac{6544515}{12424}e^{5} + \frac{1488772}{1553}e^{4} + \frac{291849}{1553}e^{3} - \frac{2846307}{12424}e^{2} - \frac{223827}{6212}e + \frac{163423}{12424}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-4w + 23]$ | $1$ |