Properties

Label 2.2.280.1-5.1-h
Base field \(\Q(\sqrt{70}) \)
Weight $[2, 2]$
Level norm $5$
Level $[5, 5, -3w + 25]$
Dimension $16$
CM no
Base change yes

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Base field \(\Q(\sqrt{70}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[5, 5, -3w + 25]$
Dimension: $16$
CM: no
Base change: yes
Newspace dimension: $88$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} + 31x^{14} + 384x^{12} + 2424x^{10} + 8252x^{8} + 14748x^{6} + 12128x^{4} + 3008x^{2} + 64\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}\frac{1}{176}e^{15} + \frac{25}{176}e^{13} + \frac{16}{11}e^{11} + \frac{719}{88}e^{9} + \frac{613}{22}e^{7} + \frac{609}{11}e^{5} + \frac{591}{11}e^{3} + \frac{173}{11}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{176}e^{15} + \frac{25}{176}e^{13} + \frac{16}{11}e^{11} + \frac{719}{88}e^{9} + \frac{613}{22}e^{7} + \frac{609}{11}e^{5} + \frac{591}{11}e^{3} + \frac{173}{11}e$
5 $[5, 5, -3w + 25]$ $\phantom{-}1$
7 $[7, 7, w]$ $-\frac{3}{88}e^{15} - \frac{43}{44}e^{13} - \frac{977}{88}e^{11} - \frac{2795}{44}e^{9} - \frac{4239}{22}e^{7} - \frac{3291}{11}e^{5} - \frac{4485}{22}e^{3} - \frac{389}{11}e$
11 $[11, 11, w - 9]$ $-\frac{1}{44}e^{14} - \frac{25}{44}e^{12} - \frac{245}{44}e^{10} - \frac{1207}{44}e^{8} - \frac{1583}{22}e^{6} - \frac{1028}{11}e^{4} - \frac{505}{11}e^{2} - \frac{54}{11}$
11 $[11, 11, -w - 9]$ $-\frac{1}{44}e^{14} - \frac{25}{44}e^{12} - \frac{245}{44}e^{10} - \frac{1207}{44}e^{8} - \frac{1583}{22}e^{6} - \frac{1028}{11}e^{4} - \frac{505}{11}e^{2} - \frac{54}{11}$
17 $[17, 17, w + 6]$ $-\frac{1}{44}e^{15} - \frac{61}{88}e^{13} - \frac{183}{22}e^{11} - \frac{4383}{88}e^{9} - \frac{1721}{11}e^{7} - \frac{11009}{44}e^{5} - \frac{3947}{22}e^{3} - \frac{450}{11}e$
17 $[17, 17, w + 11]$ $-\frac{1}{44}e^{15} - \frac{61}{88}e^{13} - \frac{183}{22}e^{11} - \frac{4383}{88}e^{9} - \frac{1721}{11}e^{7} - \frac{11009}{44}e^{5} - \frac{3947}{22}e^{3} - \frac{450}{11}e$
23 $[23, 23, w + 1]$ $\phantom{-}\frac{1}{44}e^{15} + \frac{61}{88}e^{13} + \frac{743}{88}e^{11} + \frac{2307}{44}e^{9} + \frac{3871}{22}e^{7} + \frac{6841}{22}e^{5} + \frac{5531}{22}e^{3} + \frac{593}{11}e$
23 $[23, 23, w + 22]$ $\phantom{-}\frac{1}{44}e^{15} + \frac{61}{88}e^{13} + \frac{743}{88}e^{11} + \frac{2307}{44}e^{9} + \frac{3871}{22}e^{7} + \frac{6841}{22}e^{5} + \frac{5531}{22}e^{3} + \frac{593}{11}e$
31 $[31, 31, 4w - 33]$ $\phantom{-}\frac{1}{44}e^{14} + \frac{25}{44}e^{12} + \frac{245}{44}e^{10} + \frac{1207}{44}e^{8} + \frac{797}{11}e^{6} + \frac{2155}{22}e^{4} + \frac{560}{11}e^{2} - \frac{12}{11}$
31 $[31, 31, 4w + 33]$ $\phantom{-}\frac{1}{44}e^{14} + \frac{25}{44}e^{12} + \frac{245}{44}e^{10} + \frac{1207}{44}e^{8} + \frac{797}{11}e^{6} + \frac{2155}{22}e^{4} + \frac{560}{11}e^{2} - \frac{12}{11}$
37 $[37, 37, w + 12]$ $\phantom{-}\frac{1}{88}e^{15} + \frac{9}{22}e^{13} + \frac{487}{88}e^{11} + \frac{397}{11}e^{9} + \frac{1328}{11}e^{7} + \frac{2274}{11}e^{5} + \frac{3695}{22}e^{3} + \frac{544}{11}e$
37 $[37, 37, w + 25]$ $\phantom{-}\frac{1}{88}e^{15} + \frac{9}{22}e^{13} + \frac{487}{88}e^{11} + \frac{397}{11}e^{9} + \frac{1328}{11}e^{7} + \frac{2274}{11}e^{5} + \frac{3695}{22}e^{3} + \frac{544}{11}e$
53 $[53, 53, w + 21]$ $\phantom{-}\frac{1}{22}e^{15} + \frac{111}{88}e^{13} + \frac{1211}{88}e^{11} + \frac{3283}{44}e^{9} + \frac{2298}{11}e^{7} + \frac{3101}{11}e^{5} + \frac{3109}{22}e^{3} + \frac{42}{11}e$
53 $[53, 53, w + 32]$ $\phantom{-}\frac{1}{22}e^{15} + \frac{111}{88}e^{13} + \frac{1211}{88}e^{11} + \frac{3283}{44}e^{9} + \frac{2298}{11}e^{7} + \frac{3101}{11}e^{5} + \frac{3109}{22}e^{3} + \frac{42}{11}e$
61 $[61, 61, -w - 3]$ $-\frac{3}{88}e^{14} - \frac{75}{88}e^{12} - \frac{181}{22}e^{10} - \frac{1695}{44}e^{8} - \frac{981}{11}e^{6} - \frac{959}{11}e^{4} - \frac{114}{11}e^{2} + \frac{150}{11}$
61 $[61, 61, w - 3]$ $-\frac{3}{88}e^{14} - \frac{75}{88}e^{12} - \frac{181}{22}e^{10} - \frac{1695}{44}e^{8} - \frac{981}{11}e^{6} - \frac{959}{11}e^{4} - \frac{114}{11}e^{2} + \frac{150}{11}$
73 $[73, 73, w + 17]$ $\phantom{-}\frac{7}{176}e^{15} + \frac{219}{176}e^{13} + \frac{1347}{88}e^{11} + \frac{1032}{11}e^{9} + \frac{13213}{44}e^{7} + \frac{21199}{44}e^{5} + \frac{7163}{22}e^{3} + \frac{518}{11}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -3w + 25]$ $-1$