Properties

Base field \(\Q(\sqrt{34}) \)
Weight [2, 2]
Level norm 5
Level $[5, 5, w + 2]$
Label 2.2.136.1-5.1-c
Dimension 10
CM no
Base change no

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{34}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[5, 5, w + 2]$
Label 2.2.136.1-5.1-c
Dimension 10
Is CM no
Is base change no
Parent newspace dimension 20

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} \) \(\mathstrut +\mathstrut 22x^{8} \) \(\mathstrut +\mathstrut 159x^{6} \) \(\mathstrut +\mathstrut 439x^{4} \) \(\mathstrut +\mathstrut 351x^{2} \) \(\mathstrut +\mathstrut 25\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $-\frac{77}{1339}e^{8} - \frac{1372}{1339}e^{6} - \frac{6749}{1339}e^{4} - \frac{9110}{1339}e^{2} - \frac{373}{1339}$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $-\frac{31}{6695}e^{9} + \frac{178}{6695}e^{7} + \frac{9786}{6695}e^{5} + \frac{52466}{6695}e^{3} + \frac{64174}{6695}e$
5 $[5, 5, w + 2]$ $-\frac{13}{515}e^{9} - \frac{241}{515}e^{7} - \frac{1312}{515}e^{5} - \frac{2552}{515}e^{3} - \frac{2028}{515}e$
5 $[5, 5, w + 3]$ $-\frac{3}{1339}e^{9} + \frac{190}{1339}e^{7} + \frac{3841}{1339}e^{5} + \frac{16826}{1339}e^{3} + \frac{12819}{1339}e$
11 $[11, 11, w + 1]$ $-\frac{4}{103}e^{9} - \frac{90}{103}e^{7} - \frac{681}{103}e^{5} - \frac{2045}{103}e^{3} - \frac{1757}{103}e$
11 $[11, 11, w + 10]$ $-\frac{249}{6695}e^{9} - \frac{6993}{6695}e^{7} - \frac{64151}{6695}e^{5} - \frac{204886}{6695}e^{3} - \frac{139784}{6695}e$
17 $[17, 17, -3w + 17]$ $-\frac{55}{1339}e^{8} - \frac{980}{1339}e^{6} - \frac{5012}{1339}e^{4} - \frac{8420}{1339}e^{2} - \frac{649}{1339}$
29 $[29, 29, w + 11]$ $-\frac{492}{6695}e^{9} - \frac{10349}{6695}e^{7} - \frac{70373}{6695}e^{5} - \frac{183658}{6695}e^{3} - \frac{129797}{6695}e$
29 $[29, 29, w + 18]$ $\phantom{-}\frac{461}{6695}e^{9} + \frac{10527}{6695}e^{7} + \frac{80159}{6695}e^{5} + \frac{236124}{6695}e^{3} + \frac{200666}{6695}e$
37 $[37, 37, w + 16]$ $\phantom{-}\frac{2218}{6695}e^{9} + \frac{43416}{6695}e^{7} + \frac{260452}{6695}e^{5} + \frac{559882}{6695}e^{3} + \frac{327983}{6695}e$
37 $[37, 37, w + 21]$ $-\frac{876}{6695}e^{9} - \frac{15487}{6695}e^{7} - \frac{75494}{6695}e^{5} - \frac{113414}{6695}e^{3} - \frac{81036}{6695}e$
47 $[47, 47, -w - 9]$ $\phantom{-}\frac{271}{1339}e^{8} + \frac{4707}{1339}e^{6} + \frac{21701}{1339}e^{4} + \frac{27489}{1339}e^{2} + \frac{14981}{1339}$
47 $[47, 47, w - 9]$ $-\frac{333}{1339}e^{8} - \frac{5690}{1339}e^{6} - \frac{24892}{1339}e^{4} - \frac{22982}{1339}e^{2} + \frac{891}{1339}$
49 $[49, 7, -7]$ $\phantom{-}\frac{19}{1339}e^{8} + \frac{582}{1339}e^{6} + \frac{5578}{1339}e^{4} + \frac{14838}{1339}e^{2} - \frac{2186}{1339}$
61 $[61, 61, w + 20]$ $\phantom{-}\frac{356}{6695}e^{9} + \frac{10482}{6695}e^{7} + \frac{100779}{6695}e^{5} + \frac{336299}{6695}e^{3} + \frac{254326}{6695}e$
61 $[61, 61, w + 41]$ $\phantom{-}\frac{1052}{6695}e^{9} + \frac{23979}{6695}e^{7} + \frac{179103}{6695}e^{5} + \frac{495193}{6695}e^{3} + \frac{368052}{6695}e$
89 $[89, 89, 2w - 15]$ $\phantom{-}\frac{189}{1339}e^{8} + \frac{4098}{1339}e^{6} + \frac{28495}{1339}e^{4} + \frac{67400}{1339}e^{2} + \frac{25261}{1339}$
89 $[89, 89, -2w - 15]$ $\phantom{-}\frac{216}{1339}e^{8} + \frac{3727}{1339}e^{6} + \frac{16689}{1339}e^{4} + \frac{16391}{1339}e^{2} + \frac{4959}{1339}$
103 $[103, 103, -14w + 81]$ $\phantom{-}\frac{672}{1339}e^{8} + \frac{12339}{1339}e^{6} + \frac{64865}{1339}e^{4} + \frac{106042}{1339}e^{2} + \frac{30157}{1339}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 2]$ $\frac{13}{515}e^{9} + \frac{241}{515}e^{7} + \frac{1312}{515}e^{5} + \frac{2552}{515}e^{3} + \frac{2028}{515}e$