Base field \(\Q(\sqrt{429}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 107\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, -w + 11]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 92x^{10} + 2536x^{8} - 19736x^{6} + 53956x^{4} - 41984x^{2} + 4096\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 11]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $-\frac{22297}{69728668}e^{10} + \frac{1992643}{69728668}e^{8} - \frac{25701697}{34864334}e^{6} + \frac{155681491}{34864334}e^{4} - \frac{122510208}{17432167}e^{2} - \frac{11610273}{17432167}$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1635313}{4462634752}e^{11} - \frac{37077071}{1115658688}e^{9} + \frac{494482505}{557829344}e^{7} - \frac{3417476443}{557829344}e^{5} + \frac{14586025489}{1115658688}e^{3} - \frac{186284207}{34864334}e$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{1635313}{4462634752}e^{11} + \frac{37077071}{1115658688}e^{9} - \frac{494482505}{557829344}e^{7} + \frac{3417476443}{557829344}e^{5} - \frac{14586025489}{1115658688}e^{3} + \frac{186284207}{34864334}e$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{1635313}{4462634752}e^{11} + \frac{37077071}{1115658688}e^{9} - \frac{494482505}{557829344}e^{7} + \frac{3417476443}{557829344}e^{5} - \frac{14586025489}{1115658688}e^{3} + \frac{151419873}{34864334}e$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{1635313}{4462634752}e^{11} + \frac{37077071}{1115658688}e^{9} - \frac{494482505}{557829344}e^{7} + \frac{3417476443}{557829344}e^{5} - \frac{14586025489}{1115658688}e^{3} + \frac{151419873}{34864334}e$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{3912447}{8925269504}e^{11} + \frac{88588145}{2231317376}e^{9} - \frac{1178656259}{1115658688}e^{7} + \frac{8123958157}{1115658688}e^{5} - \frac{37508919183}{2231317376}e^{3} + \frac{793365951}{69728668}e$ |
| 17 | $[17, 17, w - 10]$ | $-\frac{261347}{557829344}e^{10} + \frac{5936951}{139457336}e^{8} - \frac{159258669}{139457336}e^{6} + \frac{141737759}{17432167}e^{4} - \frac{2797361905}{139457336}e^{2} + \frac{164690192}{17432167}$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}\frac{261347}{557829344}e^{10} - \frac{5936951}{139457336}e^{8} + \frac{159258669}{139457336}e^{6} - \frac{141737759}{17432167}e^{4} + \frac{2797361905}{139457336}e^{2} - \frac{164690192}{17432167}$ |
| 19 | $[19, 19, w + 3]$ | $\phantom{-}\frac{595457}{2231317376}e^{11} - \frac{13769499}{557829344}e^{9} + \frac{192141011}{278914672}e^{7} - \frac{1559641467}{278914672}e^{5} + \frac{9236199737}{557829344}e^{3} - \frac{232114569}{17432167}e$ |
| 19 | $[19, 19, w + 15]$ | $\phantom{-}\frac{595457}{2231317376}e^{11} - \frac{13769499}{557829344}e^{9} + \frac{192141011}{278914672}e^{7} - \frac{1559641467}{278914672}e^{5} + \frac{9236199737}{557829344}e^{3} - \frac{232114569}{17432167}e$ |
| 29 | $[29, 29, -2w + 21]$ | $-\frac{353143}{557829344}e^{10} + \frac{3917313}{69728668}e^{8} - \frac{198309825}{139457336}e^{6} + \frac{549895457}{69728668}e^{4} - \frac{1469998329}{139457336}e^{2} + \frac{56336016}{17432167}$ |
| 29 | $[29, 29, 5w - 54]$ | $\phantom{-}\frac{353143}{557829344}e^{10} - \frac{3917313}{69728668}e^{8} + \frac{198309825}{139457336}e^{6} - \frac{549895457}{69728668}e^{4} + \frac{1469998329}{139457336}e^{2} - \frac{56336016}{17432167}$ |
| 47 | $[47, 47, w + 18]$ | $\phantom{-}\frac{297037}{278914672}e^{11} - \frac{13659441}{139457336}e^{9} + \frac{94048525}{34864334}e^{7} - \frac{1457149175}{69728668}e^{5} + \frac{3888147135}{69728668}e^{3} - \frac{752802056}{17432167}e$ |
| 47 | $[47, 47, w + 28]$ | $-\frac{297037}{278914672}e^{11} + \frac{13659441}{139457336}e^{9} - \frac{94048525}{34864334}e^{7} + \frac{1457149175}{69728668}e^{5} - \frac{3888147135}{69728668}e^{3} + \frac{752802056}{17432167}e$ |
| 59 | $[59, 59, w + 27]$ | $\phantom{-}\frac{2754995}{2231317376}e^{11} - \frac{63787653}{557829344}e^{9} + \frac{891311263}{278914672}e^{7} - \frac{7207021825}{278914672}e^{5} + \frac{39545628803}{557829344}e^{3} - \frac{809541565}{17432167}e$ |
| 59 | $[59, 59, w + 31]$ | $-\frac{2754995}{2231317376}e^{11} + \frac{63787653}{557829344}e^{9} - \frac{891311263}{278914672}e^{7} + \frac{7207021825}{278914672}e^{5} - \frac{39545628803}{557829344}e^{3} + \frac{809541565}{17432167}e$ |
| 71 | $[71, 71, w + 21]$ | $-\frac{378699}{2231317376}e^{11} + \frac{9149889}{557829344}e^{9} - \frac{138923063}{278914672}e^{7} + \frac{1378425125}{278914672}e^{5} - \frac{8440451723}{557829344}e^{3} + \frac{56739509}{17432167}e$ |
| 71 | $[71, 71, w + 49]$ | $\phantom{-}\frac{378699}{2231317376}e^{11} - \frac{9149889}{557829344}e^{9} + \frac{138923063}{278914672}e^{7} - \frac{1378425125}{278914672}e^{5} + \frac{8440451723}{557829344}e^{3} - \frac{56739509}{17432167}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w + 11]$ | $1$ |