Base field \(\Q(\sqrt{305}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5, 5, -4w + 37]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $108$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 27x^{14} + 293x^{12} - 1634x^{10} + 4963x^{8} - 8003x^{6} + 6247x^{4} - 2160x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{1}{64}e^{15} - \frac{29}{64}e^{13} + \frac{337}{64}e^{11} - \frac{125}{4}e^{9} + \frac{6369}{64}e^{7} - \frac{10355}{64}e^{5} + \frac{7229}{64}e^{3} - \frac{95}{4}e$ |
| 5 | $[5, 5, -4w + 37]$ | $-1$ |
| 7 | $[7, 7, w + 2]$ | $-\frac{3}{32}e^{15} + \frac{79}{32}e^{13} - \frac{827}{32}e^{11} + \frac{547}{4}e^{9} - \frac{12259}{32}e^{7} + \frac{17185}{32}e^{5} - \frac{9999}{32}e^{3} + \frac{225}{4}e$ |
| 7 | $[7, 7, w + 4]$ | $-\frac{1}{64}e^{15} + \frac{27}{64}e^{13} - \frac{293}{64}e^{11} + \frac{817}{32}e^{9} - \frac{4963}{64}e^{7} + \frac{8003}{64}e^{5} - \frac{6183}{64}e^{3} + \frac{107}{4}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{1}{16}e^{12} - \frac{11}{8}e^{10} + \frac{183}{16}e^{8} - \frac{703}{16}e^{6} + \frac{149}{2}e^{4} - \frac{651}{16}e^{2} + 5$ |
| 17 | $[17, 17, w + 6]$ | $-\frac{3}{64}e^{15} + \frac{85}{64}e^{13} - \frac{967}{64}e^{11} + \frac{2801}{32}e^{9} - \frac{17221}{64}e^{7} + \frac{26345}{64}e^{5} - \frac{16385}{64}e^{3} + \frac{191}{4}e$ |
| 17 | $[17, 17, w + 10]$ | $-\frac{3}{32}e^{15} + \frac{79}{32}e^{13} - \frac{827}{32}e^{11} + \frac{545}{4}e^{9} - \frac{12019}{32}e^{7} + \frac{16001}{32}e^{5} - \frac{7871}{32}e^{3} + \frac{111}{4}e$ |
| 19 | $[19, 19, -2w + 19]$ | $-\frac{1}{8}e^{14} + \frac{51}{16}e^{12} - 32e^{10} + \frac{2567}{16}e^{8} - \frac{6713}{16}e^{6} + \frac{4299}{8}e^{4} - \frac{4357}{16}e^{2} + 38$ |
| 19 | $[19, 19, -2w - 17]$ | $\phantom{-}\frac{1}{8}e^{14} - \frac{13}{4}e^{12} + \frac{267}{8}e^{10} - \frac{1375}{8}e^{8} + \frac{929}{2}e^{6} - \frac{4983}{8}e^{4} + 344e^{2} - 58$ |
| 23 | $[23, 23, w + 5]$ | $-\frac{3}{64}e^{15} + \frac{73}{64}e^{13} - \frac{703}{64}e^{11} + \frac{1719}{32}e^{9} - \frac{9201}{64}e^{7} + \frac{13705}{64}e^{5} - \frac{10845}{64}e^{3} + \frac{193}{4}e$ |
| 23 | $[23, 23, w + 17]$ | $\phantom{-}\frac{1}{32}e^{15} - \frac{27}{32}e^{13} + \frac{293}{32}e^{11} - \frac{809}{16}e^{9} + \frac{4723}{32}e^{7} - \frac{6787}{32}e^{5} + \frac{3767}{32}e^{3} - 11e$ |
| 37 | $[37, 37, w + 1]$ | $-\frac{11}{64}e^{15} + \frac{285}{64}e^{13} - \frac{2927}{64}e^{11} + \frac{7569}{32}e^{9} - \frac{41261}{64}e^{7} + \frac{55969}{64}e^{5} - \frac{31209}{64}e^{3} + \frac{323}{4}e$ |
| 37 | $[37, 37, w + 35]$ | $\phantom{-}\frac{11}{64}e^{15} - \frac{285}{64}e^{13} + \frac{2927}{64}e^{11} - \frac{7553}{32}e^{9} + \frac{40781}{64}e^{7} - \frac{53601}{64}e^{5} + \frac{26953}{64}e^{3} - \frac{217}{4}e$ |
| 41 | $[41, 41, -22w + 203]$ | $\phantom{-}\frac{1}{16}e^{14} - \frac{3}{2}e^{12} + \frac{227}{16}e^{10} - \frac{1085}{16}e^{8} + \frac{1403}{8}e^{6} - \frac{3867}{16}e^{4} + \frac{1243}{8}e^{2} - 31$ |
| 41 | $[41, 41, -6w + 55]$ | $-\frac{1}{8}e^{14} + \frac{49}{16}e^{12} - \frac{119}{4}e^{10} + \frac{2337}{16}e^{8} - \frac{6123}{16}e^{6} + \frac{4143}{8}e^{4} - \frac{5111}{16}e^{2} + 64$ |
| 43 | $[43, 43, w + 20]$ | $\phantom{-}\frac{1}{16}e^{15} - \frac{27}{16}e^{13} + \frac{289}{16}e^{11} - \frac{781}{8}e^{9} + \frac{4487}{16}e^{7} - \frac{6551}{16}e^{5} + \frac{4087}{16}e^{3} - \frac{157}{4}e$ |
| 43 | $[43, 43, w + 22]$ | $-\frac{13}{64}e^{15} + \frac{339}{64}e^{13} - \frac{3529}{64}e^{11} + \frac{9331}{32}e^{9} - \frac{52547}{64}e^{7} + \frac{74519}{64}e^{5} - \frac{44119}{64}e^{3} + \frac{257}{2}e$ |
| 53 | $[53, 53, w + 13]$ | $\phantom{-}\frac{5}{64}e^{15} - \frac{139}{64}e^{13} + \frac{1553}{64}e^{11} - \frac{4435}{32}e^{9} + \frac{27147}{64}e^{7} - \frac{42287}{64}e^{5} + \frac{28239}{64}e^{3} - \frac{369}{4}e$ |
| 53 | $[53, 53, w + 39]$ | $-\frac{3}{64}e^{15} + \frac{81}{64}e^{13} - \frac{879}{64}e^{11} + \frac{2451}{32}e^{9} - \frac{14889}{64}e^{7} + \frac{23945}{64}e^{5} - \frac{18037}{64}e^{3} + \frac{293}{4}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -4w + 37]$ | $1$ |