Properties

Label 722.2
Level 722
Weight 2
Dimension 5386
Nonzero newspaces 6
Newform subspaces 53
Sturm bound 64980
Trace bound 1

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Defining parameters

Level: \( N \) = \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 53 \)
Sturm bound: \(64980\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(722))\).

Total New Old
Modular forms 16749 5386 11363
Cusp forms 15742 5386 10356
Eisenstein series 1007 0 1007

Trace form

\( 5386q + q^{2} + 4q^{3} + q^{4} + 6q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + O(q^{10}) \) \( 5386q + q^{2} + 4q^{3} + q^{4} + 6q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + 6q^{10} + 12q^{11} - 8q^{12} - 34q^{13} - 28q^{14} - 48q^{15} + q^{16} - 18q^{17} - 41q^{18} - 42q^{19} - 30q^{20} - 52q^{21} - 42q^{22} - 12q^{23} + 4q^{24} - 41q^{25} - 22q^{26} - 26q^{27} - 4q^{28} - 6q^{29} + 24q^{30} - 4q^{31} + q^{32} - 60q^{33} + 18q^{34} - 24q^{35} + 13q^{36} + 2q^{37} - 52q^{39} + 6q^{40} + 6q^{41} + 32q^{42} - 40q^{43} - 6q^{44} - 138q^{45} - 48q^{46} - 96q^{47} - 14q^{48} - 63q^{49} - 113q^{50} - 126q^{51} + 2q^{52} - 90q^{53} - 68q^{54} - 72q^{55} - 64q^{56} - 90q^{57} - 42q^{58} - 120q^{59} - 48q^{60} - 94q^{61} - 76q^{62} - 88q^{63} - 11q^{64} - 132q^{65} - 96q^{66} - 88q^{67} - 12q^{69} - 24q^{70} - 72q^{71} - 5q^{72} + 8q^{73} + 38q^{74} + 40q^{75} + 24q^{77} - 16q^{78} - 76q^{79} + 6q^{80} - 77q^{81} - 30q^{82} - 60q^{83} - 76q^{84} - 36q^{85} - 28q^{86} - 240q^{87} + 12q^{88} - 54q^{89} - 102q^{90} - 80q^{91} - 48q^{92} - 172q^{93} - 96q^{94} - 90q^{95} + 4q^{96} - 82q^{97} - 87q^{98} - 258q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)

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
722.2.a \(\chi_{722}(1, \cdot)\) 722.2.a.a 1 1
722.2.a.b 1
722.2.a.c 1
722.2.a.d 1
722.2.a.e 1
722.2.a.f 1
722.2.a.g 2
722.2.a.h 2
722.2.a.i 2
722.2.a.j 2
722.2.a.k 3
722.2.a.l 3
722.2.a.m 4
722.2.a.n 4
722.2.c \(\chi_{722}(429, \cdot)\) 722.2.c.a 2 2
722.2.c.b 2
722.2.c.c 2
722.2.c.d 2
722.2.c.e 2
722.2.c.f 2
722.2.c.g 2
722.2.c.h 4
722.2.c.i 4
722.2.c.j 4
722.2.c.k 6
722.2.c.l 6
722.2.c.m 8
722.2.c.n 8
722.2.e \(\chi_{722}(99, \cdot)\) 722.2.e.a 6 6
722.2.e.b 6
722.2.e.c 6
722.2.e.d 6
722.2.e.e 6
722.2.e.f 6
722.2.e.g 6
722.2.e.h 6
722.2.e.i 6
722.2.e.j 6
722.2.e.k 6
722.2.e.l 6
722.2.e.m 6
722.2.e.n 12
722.2.e.o 12
722.2.e.p 12
722.2.e.q 12
722.2.e.r 24
722.2.e.s 24
722.2.g \(\chi_{722}(39, \cdot)\) 722.2.g.a 288 18
722.2.g.b 306
722.2.i \(\chi_{722}(7, \cdot)\) 722.2.i.a 576 36
722.2.i.b 612
722.2.k \(\chi_{722}(5, \cdot)\) 722.2.k.a 1620 108
722.2.k.b 1728

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(722))\) into lower level spaces

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