Base field \(\Q(\sqrt{161}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 40\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 8, -7w + 48]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 44x^{10} + 696x^{8} - 5024x^{6} + 17152x^{4} - 25344x^{2} + 10816\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 6]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -w + 7]$ | $-\frac{37}{6848}e^{10} + \frac{765}{3424}e^{8} - \frac{2711}{856}e^{6} + \frac{15989}{856}e^{4} - \frac{18125}{428}e^{2} + \frac{2565}{107}$ |
| 5 | $[5, 5, -6w - 35]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -6w + 41]$ | $\phantom{-}\frac{205}{22256}e^{11} - \frac{1043}{2782}e^{9} + \frac{7208}{1391}e^{7} - \frac{163945}{5564}e^{5} + \frac{178337}{2782}e^{3} - \frac{50264}{1391}e$ |
| 7 | $[7, 7, 32w - 219]$ | $-\frac{193}{89024}e^{11} + \frac{3921}{44512}e^{9} - \frac{6725}{5564}e^{7} + \frac{74443}{11128}e^{5} - \frac{73971}{5564}e^{3} + \frac{9062}{1391}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{19}{3424}e^{10} - \frac{777}{3424}e^{8} + \frac{5369}{1712}e^{6} - \frac{3725}{214}e^{4} + \frac{14465}{428}e^{2} - \frac{2397}{214}$ |
| 17 | $[17, 17, 2w - 13]$ | $-\frac{905}{89024}e^{11} + \frac{9175}{22256}e^{9} - \frac{126231}{22256}e^{7} + \frac{357519}{11128}e^{5} - \frac{195271}{2782}e^{3} + \frac{118175}{2782}e$ |
| 17 | $[17, 17, 2w + 11]$ | $-\frac{1121}{89024}e^{11} + \frac{5717}{11128}e^{9} - \frac{158225}{22256}e^{7} + \frac{447147}{11128}e^{5} - \frac{117687}{1391}e^{3} + \frac{119129}{2782}e$ |
| 19 | $[19, 19, 4w + 23]$ | $-\frac{129}{6848}e^{11} + \frac{1309}{1712}e^{9} - \frac{17987}{1712}e^{7} + \frac{50407}{856}e^{5} - \frac{26187}{214}e^{3} + \frac{11885}{214}e$ |
| 19 | $[19, 19, 4w - 27]$ | $\phantom{-}\frac{857}{89024}e^{11} - \frac{8673}{22256}e^{9} + \frac{118503}{22256}e^{7} - \frac{327401}{11128}e^{5} + \frac{81047}{1391}e^{3} - \frac{51195}{2782}e$ |
| 23 | $[23, 23, 58w - 397]$ | $\phantom{-}\frac{37}{3424}e^{10} - \frac{765}{1712}e^{8} + \frac{2711}{428}e^{6} - \frac{15989}{428}e^{4} + \frac{18125}{214}e^{2} - \frac{4916}{107}$ |
| 29 | $[29, 29, 20w - 137]$ | $-\frac{23}{3424}e^{10} + \frac{873}{3424}e^{8} - \frac{5373}{1712}e^{6} + \frac{1576}{107}e^{4} - \frac{9581}{428}e^{2} + \frac{1077}{214}$ |
| 29 | $[29, 29, -20w - 117]$ | $-\frac{19}{3424}e^{10} + \frac{777}{3424}e^{8} - \frac{5369}{1712}e^{6} + \frac{3725}{214}e^{4} - \frac{14465}{428}e^{2} + \frac{2397}{214}$ |
| 61 | $[61, 61, 2w - 11]$ | $\phantom{-}\frac{1077}{44512}e^{11} - \frac{44359}{44512}e^{9} + \frac{312019}{22256}e^{7} - \frac{227041}{2782}e^{5} + \frac{1014587}{5564}e^{3} - \frac{293973}{2782}e$ |
| 61 | $[61, 61, -2w - 9]$ | $-\frac{647}{44512}e^{11} + \frac{25907}{44512}e^{9} - \frac{173559}{22256}e^{7} + \frac{231453}{5564}e^{5} - \frac{431525}{5564}e^{3} + \frac{67151}{2782}e$ |
| 71 | $[71, 71, -10w - 59]$ | $\phantom{-}\frac{1}{32}e^{10} - \frac{41}{32}e^{8} + \frac{285}{16}e^{6} - \frac{201}{2}e^{4} + \frac{825}{4}e^{2} - \frac{185}{2}$ |
| 71 | $[71, 71, 10w - 69]$ | $\phantom{-}\frac{3}{1712}e^{10} - \frac{251}{3424}e^{8} + \frac{1825}{1712}e^{6} - \frac{2775}{428}e^{4} + \frac{5835}{428}e^{2} + \frac{375}{214}$ |
| 83 | $[83, 83, -44w + 301]$ | $\phantom{-}\frac{1617}{89024}e^{11} - \frac{32779}{44512}e^{9} + \frac{112781}{11128}e^{7} - \frac{640595}{11128}e^{5} + \frac{707113}{5564}e^{3} - \frac{109113}{1391}e$ |
| 83 | $[83, 83, 44w + 257]$ | $-\frac{627}{89024}e^{11} + \frac{12767}{44512}e^{9} - \frac{22107}{5564}e^{7} + \frac{253447}{11128}e^{5} - \frac{282703}{5564}e^{3} + \frac{39811}{1391}e$ |
| 89 | $[89, 89, -70w - 409]$ | $\phantom{-}\frac{25}{5564}e^{11} - \frac{7903}{44512}e^{9} + \frac{51881}{22256}e^{7} - \frac{33303}{2782}e^{5} + \frac{103657}{5564}e^{3} + \frac{23735}{2782}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 6]$ | $1$ |