Properties

Label 4.4.19525.1-25.1-h
Base field 4.4.19525.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -\frac{2}{3}w^{2} + \frac{5}{3}w + 5]$
Dimension $10$
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.19525.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 14x^{2} + 15x + 45\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, -\frac{2}{3}w^{2} + \frac{5}{3}w + 5]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $44$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} - 26x^{8} + 226x^{6} - 751x^{4} + 918x^{2} - 243\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $\phantom{-}0$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $\phantom{-}e$
9 $[9, 3, -w + 3]$ $-\frac{13}{765}e^{8} + \frac{55}{153}e^{6} - \frac{1723}{765}e^{4} + \frac{671}{153}e^{2} - \frac{206}{85}$
9 $[9, 3, w + 2]$ $-\frac{28}{765}e^{8} + \frac{142}{153}e^{6} - \frac{5653}{765}e^{4} + \frac{2834}{153}e^{2} - \frac{751}{85}$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $\phantom{-}\frac{4}{135}e^{9} - \frac{19}{27}e^{7} + \frac{724}{135}e^{5} - \frac{383}{27}e^{3} + \frac{188}{15}e$
16 $[16, 2, 2]$ $-\frac{41}{765}e^{8} + \frac{197}{153}e^{6} - \frac{7376}{765}e^{4} + \frac{3352}{153}e^{2} - \frac{617}{85}$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}\frac{1}{2295}e^{9} - \frac{16}{459}e^{7} + \frac{2251}{2295}e^{5} - \frac{3806}{459}e^{3} + \frac{1289}{85}e$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-\frac{28}{765}e^{9} + \frac{142}{153}e^{7} - \frac{5653}{765}e^{5} + \frac{2834}{153}e^{3} - \frac{751}{85}e$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $\phantom{-}\frac{29}{2295}e^{9} - \frac{158}{459}e^{7} + \frac{7139}{2295}e^{5} - \frac{4957}{459}e^{3} + \frac{3343}{255}e$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}\frac{58}{765}e^{9} - \frac{265}{153}e^{7} + \frac{9178}{765}e^{5} - \frac{3590}{153}e^{3} + \frac{1358}{255}e$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}\frac{29}{2295}e^{9} - \frac{158}{459}e^{7} + \frac{7139}{2295}e^{5} - \frac{4498}{459}e^{3} + \frac{1303}{255}e$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $-\frac{1}{45}e^{9} + \frac{4}{9}e^{7} - \frac{106}{45}e^{5} + \frac{5}{9}e^{3} + \frac{134}{15}e$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $\phantom{-}\frac{5}{459}e^{9} - \frac{94}{459}e^{7} + \frac{545}{459}e^{5} - \frac{1208}{459}e^{3} + \frac{23}{51}e$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $-\frac{37}{459}e^{9} + \frac{818}{459}e^{7} - \frac{5104}{459}e^{5} + \frac{5665}{459}e^{3} + \frac{877}{51}e$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $-\frac{13}{765}e^{8} + \frac{55}{153}e^{6} - \frac{1723}{765}e^{4} + \frac{518}{153}e^{2} + \frac{729}{85}$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $\phantom{-}\frac{137}{765}e^{8} - \frac{662}{153}e^{6} + \frac{23807}{765}e^{4} - \frac{9025}{153}e^{2} + \frac{909}{85}$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $\phantom{-}\frac{12}{85}e^{8} - \frac{56}{17}e^{6} + \frac{1937}{85}e^{4} - \frac{673}{17}e^{2} + \frac{116}{85}$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $\phantom{-}\frac{98}{2295}e^{9} - \frac{497}{459}e^{7} + \frac{19403}{2295}e^{5} - \frac{9307}{459}e^{3} + \frac{3266}{255}e$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $-\frac{152}{2295}e^{9} + \frac{749}{459}e^{7} - \frac{29267}{2295}e^{5} + \frac{15472}{459}e^{3} - \frac{6979}{255}e$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $-\frac{3}{85}e^{8} + \frac{14}{17}e^{6} - \frac{548}{85}e^{4} + \frac{317}{17}e^{2} - \frac{709}{85}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $1$