Base field \(\Q(\sqrt{15}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 15\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[17, 17, w + 7]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 56x^{14} + 1052x^{12} + 7680x^{10} + 23152x^{8} + 29888x^{6} + 16256x^{4} + 3584x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $-\frac{23}{1280}e^{15} - e^{13} - \frac{2969}{160}e^{11} - \frac{658}{5}e^{9} - \frac{1485}{4}e^{7} - \frac{4147}{10}e^{5} - 164e^{3} - \frac{197}{10}e$ |
| 3 | $[3, 3, w]$ | $-\frac{23}{1280}e^{15} - e^{13} - \frac{2969}{160}e^{11} - \frac{658}{5}e^{9} - \frac{1485}{4}e^{7} - \frac{4147}{10}e^{5} - 164e^{3} - \frac{187}{10}e$ |
| 5 | $[5, 5, w]$ | $-\frac{43}{2560}e^{15} - \frac{1197}{1280}e^{13} - \frac{5557}{320}e^{11} - \frac{9867}{80}e^{9} - \frac{55777}{160}e^{7} - \frac{31007}{80}e^{5} - \frac{1147}{8}e^{3} - \frac{209}{20}e$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{17}{640}e^{15} + \frac{473}{320}e^{13} + \frac{1755}{64}e^{11} + \frac{31087}{160}e^{9} + \frac{43653}{80}e^{7} + \frac{2385}{4}e^{5} + \frac{4243}{20}e^{3} + \frac{88}{5}e$ |
| 7 | $[7, 7, w + 6]$ | $\phantom{-}\frac{29}{1280}e^{15} + \frac{81}{64}e^{13} + \frac{7571}{320}e^{11} + \frac{13657}{80}e^{9} + \frac{10011}{20}e^{7} + \frac{24209}{40}e^{5} + \frac{5571}{20}e^{3} + \frac{194}{5}e$ |
| 11 | $[11, 11, -w - 2]$ | $\phantom{-}\frac{3}{160}e^{14} + \frac{167}{160}e^{12} + \frac{3101}{160}e^{10} + \frac{5509}{40}e^{8} + \frac{7817}{20}e^{6} + \frac{8889}{20}e^{4} + 183e^{2} + 20$ |
| 11 | $[11, 11, w - 2]$ | $-\frac{37}{1280}e^{14} - \frac{1029}{640}e^{12} - \frac{4769}{160}e^{10} - \frac{3375}{16}e^{8} - \frac{47377}{80}e^{6} - \frac{5231}{8}e^{4} - \frac{4957}{20}e^{2} - \frac{251}{10}$ |
| 17 | $[17, 17, w + 7]$ | $\phantom{-}\frac{69}{5120}e^{15} + \frac{1923}{2560}e^{13} + \frac{2237}{160}e^{11} + \frac{1997}{20}e^{9} + \frac{18303}{64}e^{7} + \frac{52579}{160}e^{5} + \frac{10803}{80}e^{3} + \frac{633}{40}e$ |
| 17 | $[17, 17, w + 10]$ | $\phantom{-}\frac{49}{2560}e^{15} + \frac{271}{256}e^{13} + \frac{97}{5}e^{11} + \frac{4271}{32}e^{9} + \frac{55893}{160}e^{7} + \frac{5137}{16}e^{5} + \frac{2487}{40}e^{3} - \frac{93}{20}e$ |
| 43 | $[43, 43, w + 12]$ | $\phantom{-}\frac{31}{1280}e^{15} + \frac{861}{640}e^{13} + \frac{199}{8}e^{11} + 175e^{9} + \frac{38859}{80}e^{7} + \frac{21217}{40}e^{5} + \frac{4287}{20}e^{3} + \frac{377}{10}e$ |
| 43 | $[43, 43, w + 31]$ | $-\frac{1}{32}e^{15} - \frac{139}{80}e^{13} - \frac{5149}{160}e^{11} - \frac{36351}{160}e^{9} - \frac{50703}{80}e^{7} - \frac{27527}{40}e^{5} - \frac{1256}{5}e^{3} - \frac{241}{10}e$ |
| 53 | $[53, 53, w + 11]$ | $-\frac{97}{2560}e^{15} - \frac{2703}{1280}e^{13} - \frac{393}{10}e^{11} - \frac{22457}{80}e^{9} - \frac{128947}{160}e^{7} - \frac{75171}{80}e^{5} - \frac{16431}{40}e^{3} - \frac{1009}{20}e$ |
| 53 | $[53, 53, w + 42]$ | $\phantom{-}\frac{149}{2560}e^{15} + \frac{4139}{1280}e^{13} + \frac{299}{5}e^{11} + \frac{8413}{20}e^{9} + \frac{186163}{160}e^{7} + \frac{19799}{16}e^{5} + \frac{16771}{40}e^{3} + \frac{513}{20}e$ |
| 59 | $[59, 59, 2w - 1]$ | $-\frac{19}{640}e^{14} - \frac{527}{320}e^{12} - \frac{4859}{160}e^{10} - \frac{8487}{40}e^{8} - \frac{23093}{40}e^{6} - 589e^{4} - \frac{1699}{10}e^{2} - 1$ |
| 59 | $[59, 59, -2w - 1]$ | $\phantom{-}\frac{1}{32}e^{14} + \frac{139}{80}e^{12} + \frac{5149}{160}e^{10} + \frac{4543}{20}e^{8} + \frac{5059}{8}e^{6} + \frac{2709}{4}e^{4} + \frac{1138}{5}e^{2} + \frac{99}{5}$ |
| 61 | $[61, 61, 2w - 11]$ | $\phantom{-}\frac{1}{80}e^{14} + \frac{7}{10}e^{12} + \frac{263}{20}e^{10} + \frac{3837}{40}e^{8} + 287e^{6} + \frac{1777}{5}e^{4} + \frac{812}{5}e^{2} + \frac{78}{5}$ |
| 61 | $[61, 61, -2w - 11]$ | $\phantom{-}\frac{19}{320}e^{14} + \frac{1059}{320}e^{12} + \frac{4927}{80}e^{10} + \frac{35169}{80}e^{8} + \frac{2513}{2}e^{6} + \frac{28653}{20}e^{4} + \frac{2882}{5}e^{2} + \frac{323}{5}$ |
| 67 | $[67, 67, w + 22]$ | $-\frac{9}{320}e^{15} - \frac{503}{320}e^{13} - \frac{9411}{320}e^{11} - \frac{34013}{160}e^{9} - \frac{50031}{80}e^{7} - \frac{3794}{5}e^{5} - \frac{1375}{4}e^{3} - \frac{164}{5}e$ |
| 67 | $[67, 67, w + 45]$ | $-\frac{7}{640}e^{15} - \frac{77}{128}e^{13} - \frac{109}{10}e^{11} - \frac{2331}{32}e^{9} - \frac{7029}{40}e^{7} - \frac{1191}{10}e^{5} + \frac{553}{20}e^{3} + \frac{43}{2}e$ |
| 71 | $[71, 71, 3w - 8]$ | $-\frac{3}{320}e^{14} - \frac{167}{320}e^{12} - \frac{1551}{160}e^{10} - \frac{5517}{80}e^{8} - \frac{7849}{40}e^{6} - \frac{2253}{10}e^{4} - \frac{1033}{10}e^{2} - \frac{109}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w + 7]$ | $-\frac{69}{5120}e^{15} - \frac{1923}{2560}e^{13} - \frac{2237}{160}e^{11} - \frac{1997}{20}e^{9} - \frac{18303}{64}e^{7} - \frac{52579}{160}e^{5} - \frac{10803}{80}e^{3} - \frac{633}{40}e$ |