Base field \(\Q(\sqrt{205}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[12, 6, 2w]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $68$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} + 22x^{12} + 175x^{10} + 644x^{8} + 1131x^{6} + 842x^{4} + 177x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{990}{6751}e^{13} + \frac{20858}{6751}e^{11} + \frac{155434}{6751}e^{9} + \frac{523475}{6751}e^{7} + \frac{823381}{6751}e^{5} + \frac{536815}{6751}e^{3} + \frac{91667}{6751}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 5 | $[5, 5, -w + 8]$ | $\phantom{-}\frac{1151}{33755}e^{12} + \frac{18331}{33755}e^{10} + \frac{70759}{33755}e^{8} - \frac{9446}{6751}e^{6} - \frac{538444}{33755}e^{4} - \frac{509064}{33755}e^{2} - \frac{42609}{33755}$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{3922}{33755}e^{13} - \frac{71407}{33755}e^{11} - \frac{403843}{33755}e^{9} - \frac{154882}{6751}e^{7} - \frac{155082}{33755}e^{5} + \frac{489528}{33755}e^{3} + \frac{123018}{33755}e$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{7156}{33755}e^{13} - \frac{158896}{33755}e^{11} - \frac{1282449}{33755}e^{9} - \frac{964955}{6751}e^{7} - \frac{8770371}{33755}e^{5} - \frac{6889901}{33755}e^{3} - \frac{1482521}{33755}e$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{673}{6751}e^{13} + \frac{12038}{6751}e^{11} + \frac{65826}{6751}e^{9} + \frac{119129}{6751}e^{7} + \frac{35521}{6751}e^{5} + \frac{27819}{6751}e^{3} + \frac{87812}{6751}e$ |
| 13 | $[13, 13, w + 9]$ | $-\frac{462}{33755}e^{13} - \frac{31787}{33755}e^{11} - \frac{491998}{33755}e^{9} - \frac{570935}{6751}e^{7} - \frac{6814797}{33755}e^{5} - \frac{5977612}{33755}e^{3} - \frac{1150392}{33755}e$ |
| 17 | $[17, 17, w]$ | $-\frac{166}{785}e^{13} - \frac{3381}{785}e^{11} - \frac{23904}{785}e^{9} - \frac{14989}{157}e^{7} - \frac{108746}{785}e^{5} - \frac{65161}{785}e^{3} - \frac{5756}{785}e$ |
| 17 | $[17, 17, w + 16]$ | $\phantom{-}\frac{13823}{33755}e^{13} + \frac{316368}{33755}e^{11} + \frac{2653052}{33755}e^{9} + \frac{2073260}{6751}e^{7} + \frac{19284808}{33755}e^{5} + \frac{15104713}{33755}e^{3} + \frac{3523283}{33755}e$ |
| 31 | $[31, 31, -w - 4]$ | $-\frac{3709}{6751}e^{12} - \frac{72402}{6751}e^{10} - \frac{473180}{6751}e^{8} - \frac{1283387}{6751}e^{6} - \frac{1425938}{6751}e^{4} - \frac{555636}{6751}e^{2} - \frac{43976}{6751}$ |
| 31 | $[31, 31, w - 5]$ | $-\frac{5491}{33755}e^{12} - \frac{107246}{33755}e^{10} - \frac{704354}{33755}e^{8} - \frac{388420}{6751}e^{6} - \frac{2214021}{33755}e^{4} - \frac{799546}{33755}e^{2} - \frac{69906}{33755}$ |
| 41 | $[41, 41, 3w - 22]$ | $-\frac{3442}{33755}e^{12} - \frac{59862}{33755}e^{10} - \frac{298613}{33755}e^{8} - \frac{60137}{6751}e^{6} + \frac{965058}{33755}e^{4} + \frac{1711308}{33755}e^{2} + \frac{415613}{33755}$ |
| 47 | $[47, 47, w + 19]$ | $-\frac{21423}{33755}e^{13} - \frac{459783}{33755}e^{11} - \frac{3531577}{33755}e^{9} - \frac{2492104}{6751}e^{7} - \frac{20986733}{33755}e^{5} - \frac{15074193}{33755}e^{3} - \frac{2963393}{33755}e$ |
| 47 | $[47, 47, w + 27]$ | $\phantom{-}\frac{549}{33755}e^{13} + \frac{23964}{33755}e^{11} + \frac{321621}{33755}e^{9} + \frac{348658}{6751}e^{7} + \frac{3914894}{33755}e^{5} + \frac{2929044}{33755}e^{3} - \frac{53316}{33755}e$ |
| 53 | $[53, 53, w + 14]$ | $\phantom{-}\frac{155}{6751}e^{13} + \frac{1970}{6751}e^{11} - \frac{759}{6751}e^{9} - \frac{80850}{6751}e^{7} - \frac{314232}{6751}e^{5} - \frac{421494}{6751}e^{3} - \frac{174642}{6751}e$ |
| 53 | $[53, 53, w + 38]$ | $-\frac{7002}{6751}e^{13} - \frac{152801}{6751}e^{11} - \frac{1201712}{6751}e^{9} - \frac{4361539}{6751}e^{7} - \frac{7545177}{6751}e^{5} - \frac{5520706}{6751}e^{3} - \frac{1146314}{6751}e$ |
| 59 | $[59, 59, -w - 10]$ | $-\frac{1642}{6751}e^{12} - \frac{31758}{6751}e^{10} - \frac{204420}{6751}e^{8} - \frac{544453}{6751}e^{6} - \frac{613273}{6751}e^{4} - \frac{282491}{6751}e^{2} - \frac{31447}{6751}$ |
| 59 | $[59, 59, w - 11]$ | $-\frac{2886}{33755}e^{12} - \frac{51271}{33755}e^{10} - \frac{277424}{33755}e^{8} - \frac{99194}{6751}e^{6} - \frac{164431}{33755}e^{4} - \frac{265841}{33755}e^{2} - \frac{411981}{33755}$ |
| 61 | $[61, 61, 2w - 13]$ | $-\frac{24794}{33755}e^{12} - \frac{468219}{33755}e^{10} - \frac{2865406}{33755}e^{8} - \frac{1352090}{6751}e^{6} - \frac{5257794}{33755}e^{4} - \frac{351044}{33755}e^{2} + \frac{101456}{33755}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-\frac{990}{6751}e^{13} - \frac{20858}{6751}e^{11} - \frac{155434}{6751}e^{9} - \frac{523475}{6751}e^{7} - \frac{823381}{6751}e^{5} - \frac{536815}{6751}e^{3} - \frac{91667}{6751}e$ |
| $4$ | $[4, 2, 2]$ | $1$ |