Properties

Label 3.3.1957.1-5.1-f
Base field 3.3.1957.1
Weight $[2, 2, 2]$
Level norm $5$
Level $[5, 5, w]$
Dimension $14$
CM no
Base change no

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Base field 3.3.1957.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2, 2]$
Level: $[5, 5, w]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $40$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} + 25x^{12} + 248x^{10} + 1239x^{8} + 3255x^{6} + 4264x^{4} + 2409x^{2} + 441\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{2}]$ $\phantom{-}e$
4 $[4, 2, w^{2} + w + 1]$ $-\frac{307}{3339}e^{13} - \frac{6205}{3339}e^{11} - \frac{46316}{3339}e^{9} - \frac{2490}{53}e^{7} - \frac{11438}{159}e^{5} - \frac{156652}{3339}e^{3} - \frac{13225}{1113}e$
5 $[5, 5, w]$ $-\frac{190}{10017}e^{13} - \frac{4036}{10017}e^{11} - \frac{33113}{10017}e^{9} - \frac{706}{53}e^{7} - \frac{13124}{477}e^{5} - \frac{268360}{10017}e^{3} - \frac{27298}{3339}e$
11 $[11, 11, 10w + 4]$ $-\frac{190}{3339}e^{13} - \frac{4036}{3339}e^{11} - \frac{33113}{3339}e^{9} - \frac{2118}{53}e^{7} - \frac{13124}{159}e^{5} - \frac{271699}{3339}e^{3} - \frac{31750}{1113}e$
13 $[13, 13, 12w^{2} + w + 7]$ $\phantom{-}\frac{1}{63}e^{13} + \frac{4}{63}e^{11} - \frac{151}{63}e^{9} - 24e^{7} - \frac{244}{3}e^{5} - \frac{6572}{63}e^{3} - \frac{800}{21}e$
17 $[17, 17, w + 1]$ $-\frac{19}{53}e^{12} - \frac{393}{53}e^{10} - \frac{3041}{53}e^{8} - \frac{10916}{53}e^{6} - \frac{18349}{53}e^{4} - \frac{13268}{53}e^{2} - \frac{3006}{53}$
17 $[17, 17, 16w^{2} + 16]$ $-\frac{734}{3339}e^{13} - \frac{15662}{3339}e^{11} - \frac{126550}{3339}e^{9} - \frac{7665}{53}e^{7} - \frac{42094}{159}e^{5} - \frac{706859}{3339}e^{3} - \frac{61616}{1113}e$
17 $[17, 17, 16w^{2} + 16w + 8]$ $\phantom{-}\frac{232}{1113}e^{13} + \frac{4729}{1113}e^{11} + \frac{35969}{1113}e^{9} + \frac{6033}{53}e^{7} + \frac{9987}{53}e^{5} + \frac{154288}{1113}e^{3} + \frac{13228}{371}e$
19 $[19, 19, 18w^{2} + 18w + 1]$ $-\frac{856}{3339}e^{13} - \frac{17410}{3339}e^{11} - \frac{130871}{3339}e^{9} - \frac{7069}{53}e^{7} - \frac{32000}{159}e^{5} - \frac{386584}{3339}e^{3} - \frac{17566}{1113}e$
19 $[19, 19, -w^{2} + 7]$ $\phantom{-}\frac{13}{159}e^{12} + \frac{241}{159}e^{10} + \frac{1520}{159}e^{8} + \frac{1133}{53}e^{6} - \frac{57}{53}e^{4} - \frac{6476}{159}e^{2} - \frac{910}{53}$
25 $[25, 5, 4w^{2} + w + 4]$ $\phantom{-}\frac{37}{477}e^{13} + \frac{796}{477}e^{11} + \frac{6491}{477}e^{9} + \frac{2794}{53}e^{7} + \frac{15962}{159}e^{5} + \frac{42343}{477}e^{3} + \frac{3823}{159}e$
27 $[27, 3, -3]$ $\phantom{-}\frac{10}{159}e^{12} + \frac{271}{159}e^{10} + \frac{2747}{159}e^{8} + \frac{4341}{53}e^{6} + \frac{9806}{53}e^{4} + \frac{28384}{159}e^{2} + \frac{2745}{53}$
29 $[29, 29, w + 7]$ $-\frac{842}{3339}e^{13} - \frac{17921}{3339}e^{11} - \frac{144388}{3339}e^{9} - \frac{8730}{53}e^{7} - \frac{48133}{159}e^{5} - \frac{825659}{3339}e^{3} - \frac{74567}{1113}e$
41 $[41, 41, 40w^{2} + 18]$ $\phantom{-}\frac{26}{477}e^{13} + \frac{482}{477}e^{11} + \frac{3040}{477}e^{9} + \frac{773}{53}e^{7} + \frac{628}{159}e^{5} - \frac{4525}{477}e^{3} + \frac{194}{159}e$
43 $[43, 43, w^{2} - 11]$ $-\frac{16}{53}e^{12} - \frac{317}{53}e^{10} - \frac{2307}{53}e^{8} - \frac{7555}{53}e^{6} - \frac{10997}{53}e^{4} - \frac{6576}{53}e^{2} - \frac{1516}{53}$
47 $[47, 47, 2w^{2} + 2w - 13]$ $\phantom{-}\frac{22}{159}e^{12} + \frac{469}{159}e^{10} + \frac{3722}{159}e^{8} + \frac{4494}{53}e^{6} + \frac{7348}{53}e^{4} + \frac{15031}{159}e^{2} + \frac{1534}{53}$
59 $[59, 59, w^{2} - 3]$ $-\frac{173}{159}e^{12} - \frac{3464}{159}e^{10} - \frac{25597}{159}e^{8} - \frac{28560}{53}e^{6} - \frac{42783}{53}e^{4} - \frac{77675}{159}e^{2} - \frac{5168}{53}$
73 $[73, 73, w^{2} + 2w - 1]$ $-\frac{35}{53}e^{12} - \frac{710}{53}e^{10} - \frac{5348}{53}e^{8} - \frac{18418}{53}e^{6} - \frac{28657}{53}e^{4} - \frac{17406}{53}e^{2} - \frac{2932}{53}$
79 $[79, 79, w^{2} + 37]$ $\phantom{-}\frac{356}{1113}e^{13} + \frac{7199}{1113}e^{11} + \frac{54100}{1113}e^{9} + \frac{8924}{53}e^{7} + \frac{14518}{53}e^{5} + \frac{225392}{1113}e^{3} + \frac{20183}{371}e$
97 $[97, 97, w^{2} + 2w - 7]$ $-\frac{40}{53}e^{12} - \frac{819}{53}e^{10} - \frac{6271}{53}e^{8} - \frac{22306}{53}e^{6} - \frac{37271}{53}e^{4} - \frac{26828}{53}e^{2} - \frac{6493}{53}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w]$ $\frac{190}{10017}e^{13} + \frac{4036}{10017}e^{11} + \frac{33113}{10017}e^{9} + \frac{706}{53}e^{7} + \frac{13124}{477}e^{5} + \frac{268360}{10017}e^{3} + \frac{27298}{3339}e$