Properties

Label 722.6
Level 722
Weight 6
Dimension 26925
Nonzero newspaces 6
Sturm bound 194940
Trace bound 1

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Defining parameters

Level: \( N \) = \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(194940\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(722))\).

Total New Old
Modular forms 81729 26925 54804
Cusp forms 80721 26925 53796
Eisenstein series 1008 0 1008

Trace form

\( 26925q + O(q^{10}) \) \( 26925q - 1728q^{12} + 8688q^{13} + 7920q^{14} + 7128q^{15} - 8604q^{17} - 17496q^{18} - 12810q^{19} - 6336q^{20} + 3780q^{21} + 17064q^{22} + 20556q^{23} + 46728q^{25} + 7920q^{26} - 82314q^{27} - 28608q^{28} + 22716q^{29} + 39276q^{31} + 25812q^{33} - 59112q^{35} - 49284q^{37} - 115452q^{39} + 1116q^{41} + 4620q^{43} - 65952q^{44} + 236304q^{45} + 121248q^{46} + 354384q^{47} + 50688q^{48} + 130800q^{49} + 230976q^{50} - 90702q^{51} - 5568q^{52} - 210096q^{53} - 246672q^{54} - 411984q^{55} - 225792q^{56} - 277110q^{57} - 193248q^{58} - 354420q^{59} - 70272q^{60} - 42252q^{61} + 168048q^{62} + 536832q^{63} + 49152q^{64} + 1091520q^{65} + 783936q^{66} + 744132q^{67} + 72288q^{68} + 179388q^{69} - 155232q^{70} - 904032q^{71} - 277632q^{72} - 548034q^{73} - 472500q^{75} - 997632q^{77} - 843552q^{78} - 482172q^{79} + 904194q^{81} + 573408q^{82} + 1106928q^{83} + 879552q^{84} + 989136q^{85} + 361440q^{86} + 1479960q^{87} + 13752q^{89} - 726480q^{90} - 1038912q^{91} - 531072q^{92} - 2689596q^{93} - 1272384q^{94} - 1251810q^{95} - 774396q^{97} - 742464q^{98} + 395082q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(722))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
722.6.a \(\chi_{722}(1, \cdot)\) 722.6.a.a 1 1
722.6.a.b 1
722.6.a.c 2
722.6.a.d 3
722.6.a.e 3
722.6.a.f 3
722.6.a.g 4
722.6.a.h 4
722.6.a.i 4
722.6.a.j 4
722.6.a.k 6
722.6.a.l 6
722.6.a.m 8
722.6.a.n 8
722.6.a.o 12
722.6.a.p 12
722.6.a.q 15
722.6.a.r 15
722.6.a.s 16
722.6.a.t 16
722.6.c \(\chi_{722}(429, \cdot)\) n/a 286 2
722.6.e \(\chi_{722}(99, \cdot)\) n/a 846 6
722.6.g \(\chi_{722}(39, \cdot)\) n/a 2826 18
722.6.i \(\chi_{722}(7, \cdot)\) n/a 5652 36
722.6.k \(\chi_{722}(5, \cdot)\) n/a 17172 108

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(722))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(722)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)