Base field 5.5.122821.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[19, 19, w^{4} - 2w^{3} - 3w^{2} + w + 2]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 6x^{11} - 15x^{10} + 138x^{9} + 7x^{8} - 1150x^{7} + 931x^{6} + 3958x^{5} - 5428x^{4} - 3676x^{3} + 9096x^{2} - 4288x + 560\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{4} - 2w^{3} - 3w^{2} + 2w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $\phantom{-}\frac{29}{1904}e^{11} - \frac{149}{1904}e^{10} - \frac{253}{952}e^{9} + \frac{1549}{952}e^{8} + \frac{3005}{1904}e^{7} - \frac{23521}{1904}e^{6} - \frac{1555}{476}e^{5} + \frac{19343}{476}e^{4} - \frac{53}{28}e^{3} - \frac{5987}{119}e^{2} + \frac{1516}{119}e + \frac{80}{17}$ |
| 11 | $[11, 11, -w^{2} + w + 2]$ | $\phantom{-}\frac{1}{136}e^{11} + \frac{3}{68}e^{10} - \frac{12}{17}e^{9} + \frac{37}{68}e^{8} + \frac{1337}{136}e^{7} - \frac{293}{17}e^{6} - \frac{737}{17}e^{5} + \frac{3659}{34}e^{4} + \frac{103}{4}e^{3} - \frac{6699}{34}e^{2} + \frac{2372}{17}e - \frac{445}{17}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{476}e^{11} + \frac{10}{119}e^{10} - \frac{317}{476}e^{9} - \frac{41}{119}e^{8} + \frac{5077}{476}e^{7} - \frac{2447}{238}e^{6} - \frac{26177}{476}e^{5} + \frac{20493}{238}e^{4} + \frac{528}{7}e^{3} - \frac{21421}{119}e^{2} + \frac{8297}{119}e - \frac{132}{17}$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + w - 3]$ | $\phantom{-}\frac{5}{119}e^{11} - \frac{38}{119}e^{10} - \frac{33}{476}e^{9} + \frac{2551}{476}e^{8} - \frac{1709}{238}e^{7} - \frac{3526}{119}e^{6} + \frac{28025}{476}e^{5} + \frac{25633}{476}e^{4} - \frac{2085}{14}e^{3} + \frac{575}{119}e^{2} + \frac{10169}{119}e - \frac{362}{17}$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 3w^{2} + w + 2]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w^{4} - 3w^{3} - w^{2} + 5w - 3]$ | $\phantom{-}\frac{3}{952}e^{11} + \frac{1}{952}e^{10} - \frac{237}{952}e^{9} + \frac{349}{476}e^{8} + \frac{2617}{952}e^{7} - \frac{11469}{952}e^{6} - \frac{4989}{952}e^{5} + \frac{30063}{476}e^{4} - \frac{1081}{28}e^{3} - \frac{24041}{238}e^{2} + \frac{15004}{119}e - \frac{487}{17}$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 2w - 2]$ | $-e^{3} + 2e^{2} + 7e - 8$ |
| 29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 4w - 1]$ | $-\frac{1}{119}e^{11} + \frac{37}{952}e^{10} + \frac{39}{238}e^{9} - \frac{415}{476}e^{8} - \frac{435}{476}e^{7} + \frac{6903}{952}e^{6} - \frac{845}{476}e^{5} - \frac{12219}{476}e^{4} + \frac{431}{14}e^{3} + \frac{3336}{119}e^{2} - \frac{8079}{119}e + \frac{358}{17}$ |
| 37 | $[37, 37, w^{4} - 3w^{3} - w^{2} + 5w]$ | $-\frac{13}{952}e^{11} + \frac{75}{952}e^{10} + \frac{75}{952}e^{9} - \frac{481}{476}e^{8} + \frac{877}{952}e^{7} + \frac{1861}{952}e^{6} - \frac{6465}{952}e^{5} + \frac{8005}{476}e^{4} + \frac{55}{28}e^{3} - \frac{6598}{119}e^{2} + \frac{4796}{119}e - \frac{26}{17}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 4w^{2} + 3w + 1]$ | $\phantom{-}\frac{23}{952}e^{11} - \frac{135}{476}e^{10} + \frac{341}{476}e^{9} + \frac{723}{238}e^{8} - \frac{14843}{952}e^{7} + \frac{299}{119}e^{6} + \frac{39007}{476}e^{5} - \frac{51547}{476}e^{4} - \frac{1219}{14}e^{3} + \frac{31940}{119}e^{2} - \frac{21145}{119}e + \frac{454}{17}$ |
| 49 | $[49, 7, -2w^{3} + 4w^{2} + 6w - 5]$ | $-\frac{83}{952}e^{11} + \frac{61}{119}e^{10} + \frac{845}{952}e^{9} - \frac{2071}{238}e^{8} + \frac{821}{952}e^{7} + \frac{11527}{238}e^{6} - \frac{27381}{952}e^{5} - \frac{21089}{238}e^{4} + \frac{1595}{28}e^{3} + \frac{1273}{238}e^{2} + \frac{5118}{119}e - \frac{149}{17}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + w^{2} - 7w + 3]$ | $\phantom{-}\frac{65}{952}e^{11} - \frac{247}{476}e^{10} + \frac{101}{952}e^{9} + \frac{869}{119}e^{8} - \frac{12715}{952}e^{7} - \frac{11733}{476}e^{6} + \frac{80163}{952}e^{5} - \frac{9243}{238}e^{4} - \frac{3215}{28}e^{3} + \frac{50867}{238}e^{2} - \frac{16126}{119}e + \frac{368}{17}$ |
| 67 | $[67, 67, w^{3} - 2w^{2} - w + 3]$ | $\phantom{-}\frac{45}{952}e^{11} - \frac{171}{476}e^{10} + \frac{67}{476}e^{9} + \frac{565}{119}e^{8} - \frac{9773}{952}e^{7} - \frac{2757}{238}e^{6} + \frac{29401}{476}e^{5} - \frac{27435}{476}e^{4} - \frac{489}{7}e^{3} + \frac{23837}{119}e^{2} - \frac{16986}{119}e + \frac{362}{17}$ |
| 67 | $[67, 67, -w^{4} + 3w^{3} + 2w^{2} - 6w - 1]$ | $-\frac{3}{34}e^{11} + \frac{81}{136}e^{10} + \frac{81}{136}e^{9} - \frac{179}{17}e^{8} + \frac{128}{17}e^{7} + \frac{8629}{136}e^{6} - \frac{11171}{136}e^{5} - \frac{9599}{68}e^{4} + \frac{955}{4}e^{3} + \frac{958}{17}e^{2} - \frac{3083}{17}e + \frac{852}{17}$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 4]$ | $-\frac{5}{476}e^{11} + \frac{19}{238}e^{10} + \frac{19}{238}e^{9} - \frac{423}{238}e^{8} + \frac{795}{476}e^{7} + \frac{3191}{238}e^{6} - \frac{2473}{119}e^{5} - \frac{9169}{238}e^{4} + \frac{496}{7}e^{3} + \frac{3099}{119}e^{2} - \frac{7570}{119}e + \frac{320}{17}$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 8w - 2]$ | $-\frac{87}{952}e^{11} + \frac{447}{952}e^{10} + \frac{759}{476}e^{9} - \frac{2383}{238}e^{8} - \frac{7825}{952}e^{7} + \frac{73419}{952}e^{6} + \frac{12}{119}e^{5} - \frac{119033}{476}e^{4} + \frac{2901}{28}e^{3} + \frac{65775}{238}e^{2} - \frac{23852}{119}e + \frac{489}{17}$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 6w - 2]$ | $\phantom{-}\frac{3}{56}e^{11} - \frac{13}{56}e^{10} - \frac{31}{28}e^{9} + \frac{139}{28}e^{8} + \frac{475}{56}e^{7} - \frac{2173}{56}e^{6} - \frac{187}{7}e^{5} + \frac{1833}{14}e^{4} + \frac{108}{7}e^{3} - \frac{1132}{7}e^{2} + \frac{367}{7}e + 2$ |
| 103 | $[103, 103, w^{3} - 3w^{2} - 2w + 2]$ | $\phantom{-}\frac{7}{68}e^{11} - \frac{69}{136}e^{10} - \frac{32}{17}e^{9} + \frac{739}{68}e^{8} + \frac{185}{17}e^{7} - \frac{11447}{136}e^{6} - \frac{727}{68}e^{5} + \frac{18795}{68}e^{4} - 89e^{3} - \frac{5396}{17}e^{2} + \frac{3424}{17}e - \frac{348}{17}$ |
| 113 | $[113, 113, -2w^{4} + 4w^{3} + 7w^{2} - 7w - 2]$ | $-\frac{15}{136}e^{11} + \frac{10}{17}e^{10} + \frac{125}{68}e^{9} - \frac{861}{68}e^{8} - \frac{1049}{136}e^{7} + \frac{6751}{68}e^{6} - \frac{1425}{68}e^{5} - \frac{11331}{34}e^{4} + 215e^{3} + \frac{6578}{17}e^{2} - \frac{6646}{17}e + \frac{1320}{17}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w^{4} - 2w^{3} - 3w^{2} + w + 2]$ | $-1$ |