# Properties

 Label 4.4.16997.1-25.1-k Base field 4.4.16997.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, -w^{3} + 4w]$ Dimension $10$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16997.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} - x + 5$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[25, 5, -w^{3} + 4w]$ Dimension: $10$ CM: no Base change: no Newspace dimension: $39$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{10} - 5x^{9} - 32x^{8} + 166x^{7} + 255x^{6} - 1555x^{5} - 220x^{4} + 5034x^{3} - 2076x^{2} - 4808x + 3056$$
Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}1$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}1$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 3]$ $-\frac{994121}{44377688}e^{9} + \frac{3209017}{44377688}e^{8} + \frac{18419171}{22188844}e^{7} - \frac{48522135}{22188844}e^{6} - \frac{405263051}{44377688}e^{5} + \frac{749568883}{44377688}e^{4} + \frac{700651879}{22188844}e^{3} - \frac{998116831}{22188844}e^{2} - \frac{169536415}{5547211}e + \frac{201802122}{5547211}$
13 $[13, 13, w^{2} - w - 4]$ $\phantom{-}\frac{1628829}{221888440}e^{9} - \frac{6360183}{221888440}e^{8} - \frac{30534561}{110944220}e^{7} + \frac{105675519}{110944220}e^{6} + \frac{708885079}{221888440}e^{5} - \frac{1964248693}{221888440}e^{4} - \frac{1500667597}{110944220}e^{3} + \frac{3020651727}{110944220}e^{2} + \frac{494901836}{27736055}e - \frac{629558891}{27736055}$
16 $[16, 2, 2]$ $\phantom{-}\frac{1593779}{221888440}e^{9} - \frac{5827313}{221888440}e^{8} - \frac{7324359}{27736055}e^{7} + \frac{92596929}{110944220}e^{6} + \frac{645458429}{221888440}e^{5} - \frac{1572637463}{221888440}e^{4} - \frac{594787961}{55472110}e^{3} + \frac{2088622887}{110944220}e^{2} + \frac{651037427}{55472110}e - \frac{228115891}{27736055}$
19 $[19, 19, -w^{2} + w + 1]$ $\phantom{-}\frac{1008327}{221888440}e^{9} - \frac{5257709}{221888440}e^{8} - \frac{16285463}{110944220}e^{7} + \frac{86102837}{110944220}e^{6} + \frac{287961457}{221888440}e^{5} - \frac{1531418219}{221888440}e^{4} - \frac{410904341}{110944220}e^{3} + \frac{2018806411}{110944220}e^{2} + \frac{33078623}{27736055}e - \frac{264731083}{27736055}$
23 $[23, 23, -w^{3} + 4w + 2]$ $-\frac{1285389}{110944220}e^{9} + \frac{899962}{27736055}e^{8} + \frac{12430913}{27736055}e^{7} - \frac{27129547}{27736055}e^{6} - \frac{576830909}{110944220}e^{5} + \frac{426013659}{55472110}e^{4} + \frac{1008957127}{55472110}e^{3} - \frac{1329923577}{55472110}e^{2} - \frac{399201967}{27736055}e + \frac{647233777}{27736055}$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $-\frac{1305021}{27736055}e^{9} + \frac{17934013}{110944220}e^{8} + \frac{194142877}{110944220}e^{7} - \frac{279547269}{55472110}e^{6} - \frac{1086682757}{55472110}e^{5} + \frac{4610101623}{110944220}e^{4} + \frac{8063057819}{110944220}e^{3} - \frac{6491764237}{55472110}e^{2} - \frac{4418668659}{55472110}e + \frac{2624481182}{27736055}$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $-\frac{2278491}{221888440}e^{9} + \frac{5342077}{221888440}e^{8} + \frac{46050289}{110944220}e^{7} - \frac{75449941}{110944220}e^{6} - \frac{1162477041}{221888440}e^{5} + \frac{981991347}{221888440}e^{4} + \frac{2491406293}{110944220}e^{3} - \frac{1190965043}{110944220}e^{2} - \frac{811325689}{27736055}e + \frac{355351739}{27736055}$
29 $[29, 29, -w + 3]$ $\phantom{-}\frac{1497285}{44377688}e^{9} - \frac{4831933}{44377688}e^{8} - \frac{28518793}{22188844}e^{7} + \frac{75149297}{22188844}e^{6} + \frac{662597079}{44377688}e^{5} - \frac{1236342579}{44377688}e^{4} - \frac{1284178497}{22188844}e^{3} + \frac{1755865223}{22188844}e^{2} + \frac{353248834}{5547211}e - \frac{346091832}{5547211}$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $-\frac{805381}{27736055}e^{9} + \frac{9184543}{110944220}e^{8} + \frac{125071377}{110944220}e^{7} - \frac{138282529}{55472110}e^{6} - \frac{370199661}{27736055}e^{5} + \frac{2129341723}{110944220}e^{4} + \frac{5698896469}{110944220}e^{3} - \frac{1484858771}{27736055}e^{2} - \frac{3127564849}{55472110}e + \frac{1313909572}{27736055}$
37 $[37, 37, w^{3} - 4w - 1]$ $-\frac{435247}{27736055}e^{9} + \frac{5908191}{110944220}e^{8} + \frac{33254897}{55472110}e^{7} - \frac{47312379}{27736055}e^{6} - \frac{196392097}{27736055}e^{5} + \frac{1675020321}{110944220}e^{4} + \frac{1623479249}{55472110}e^{3} - \frac{1369039837}{27736055}e^{2} - \frac{974840619}{27736055}e + \frac{1402766564}{27736055}$
37 $[37, 37, w^{3} - 3w + 1]$ $\phantom{-}\frac{259433}{110944220}e^{9} - \frac{1165051}{110944220}e^{8} - \frac{1984896}{27736055}e^{7} + \frac{9044244}{27736055}e^{6} + \frac{48832773}{110944220}e^{5} - \frac{301544671}{110944220}e^{4} + \frac{77135741}{55472110}e^{3} + \frac{470718259}{55472110}e^{2} - \frac{174773071}{27736055}e - \frac{103066134}{27736055}$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $\phantom{-}\frac{2473649}{221888440}e^{9} - \frac{6558673}{221888440}e^{8} - \frac{50224331}{110944220}e^{7} + \frac{103146679}{110944220}e^{6} + \frac{1283175319}{221888440}e^{5} - \frac{1818622423}{221888440}e^{4} - \frac{2836054157}{110944220}e^{3} + \frac{3457352937}{110944220}e^{2} + \frac{969498051}{27736055}e - \frac{1027091261}{27736055}$
59 $[59, 59, w^{2} + w - 4]$ $\phantom{-}\frac{907907}{221888440}e^{9} - \frac{233339}{221888440}e^{8} - \frac{18201203}{110944220}e^{7} - \frac{15655483}{110944220}e^{6} + \frac{420556517}{221888440}e^{5} + \frac{966988031}{221888440}e^{4} - \frac{553164981}{110944220}e^{3} - \frac{2566311359}{110944220}e^{2} - \frac{20313437}{27736055}e + \frac{798614447}{27736055}$
61 $[61, 61, -2w^{2} + w + 8]$ $-\frac{237348}{5547211}e^{9} + \frac{3071847}{22188844}e^{8} + \frac{17611961}{11094422}e^{7} - \frac{23264231}{5547211}e^{6} - \frac{193291471}{11094422}e^{5} + \frac{718260601}{22188844}e^{4} + \frac{326146095}{5547211}e^{3} - \frac{467306583}{5547211}e^{2} - \frac{287315300}{5547211}e + \frac{343425978}{5547211}$
73 $[73, 73, -w^{3} + 5w - 1]$ $\phantom{-}\frac{609789}{221888440}e^{9} - \frac{6504223}{221888440}e^{8} - \frac{1104639}{27736055}e^{7} + \frac{113987969}{110944220}e^{6} - \frac{138734121}{221888440}e^{5} - \frac{2305310053}{221888440}e^{4} + \frac{196973832}{27736055}e^{3} + \frac{3601564017}{110944220}e^{2} - \frac{910471103}{55472110}e - \frac{610672431}{27736055}$
79 $[79, 79, 2w^{2} + w - 6]$ $-\frac{280427}{44377688}e^{9} + \frac{1487391}{44377688}e^{8} + \frac{4505051}{22188844}e^{7} - \frac{24148051}{22188844}e^{6} - \frac{78356405}{44377688}e^{5} + \frac{416219789}{44377688}e^{4} + \frac{106833669}{22188844}e^{3} - \frac{489393699}{22188844}e^{2} - \frac{13327098}{5547211}e + \frac{55411051}{5547211}$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $-\frac{1022161}{44377688}e^{9} + \frac{3635313}{44377688}e^{8} + \frac{19408871}{22188844}e^{7} - \frac{58985007}{22188844}e^{6} - \frac{456004371}{44377688}e^{5} + \frac{1062857867}{44377688}e^{4} + \frac{949525219}{22188844}e^{3} - \frac{1677173371}{22188844}e^{2} - \frac{293948491}{5547211}e + \frac{362087403}{5547211}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w]$ $-1$
$5$ $[5, 5, -w^{2} + w + 2]$ $-1$