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Properties

Label 702.2
Level 702
Weight 2
Dimension 3540
Nonzero newspaces 24
Newform subspaces 78
Sturm bound 54432
Trace bound 27

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Defining parameters

Level: \( N \) = \( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 78 \)
Sturm bound: \(54432\)
Trace bound: \(27\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(702))\).

Total New Old
Modular forms 14328 3540 10788
Cusp forms 12889 3540 9349
Eisenstein series 1439 0 1439

Trace form

\( 3540 q - 2 q^{2} - 2 q^{4} + 12 q^{5} + 12 q^{6} + 8 q^{7} + 10 q^{8} + 24 q^{9} + O(q^{10}) \) \( 3540 q - 2 q^{2} - 2 q^{4} + 12 q^{5} + 12 q^{6} + 8 q^{7} + 10 q^{8} + 24 q^{9} + 12 q^{10} + 36 q^{11} + 6 q^{12} + 10 q^{13} + 8 q^{14} + 36 q^{15} - 2 q^{16} + 12 q^{17} - 12 q^{18} - 4 q^{19} - 24 q^{20} - 48 q^{21} - 36 q^{23} + 10 q^{25} - 32 q^{26} - 54 q^{27} + 4 q^{28} - 24 q^{29} - 72 q^{30} + 64 q^{31} - 2 q^{32} - 54 q^{33} + 60 q^{34} + 108 q^{35} - 12 q^{36} + 64 q^{37} + 98 q^{38} + 42 q^{39} + 12 q^{40} + 108 q^{41} + 48 q^{42} + 112 q^{43} + 48 q^{44} + 48 q^{46} + 84 q^{47} + 12 q^{48} + 110 q^{49} + 130 q^{50} + 18 q^{52} + 96 q^{53} + 72 q^{54} + 36 q^{55} + 8 q^{56} + 18 q^{57} + 36 q^{58} - 18 q^{59} + 36 q^{60} + 20 q^{61} + 32 q^{62} + 12 q^{63} + 10 q^{64} + 66 q^{65} - 52 q^{67} + 30 q^{68} - 36 q^{69} - 84 q^{70} - 48 q^{72} + 116 q^{73} - 52 q^{74} - 24 q^{75} - 46 q^{76} + 24 q^{77} - 36 q^{78} - 136 q^{79} - 24 q^{80} - 60 q^{82} + 96 q^{83} - 48 q^{85} - 52 q^{86} - 72 q^{87} - 54 q^{88} + 102 q^{89} - 36 q^{90} + 50 q^{91} + 12 q^{93} - 60 q^{94} + 36 q^{95} - 12 q^{96} - 128 q^{97} - 222 q^{98} - 144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(702))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
702.2.a \(\chi_{702}(1, \cdot)\) 702.2.a.a 1 1
702.2.a.b 1
702.2.a.c 1
702.2.a.d 1
702.2.a.e 1
702.2.a.f 1
702.2.a.g 1
702.2.a.h 1
702.2.a.i 1
702.2.a.j 1
702.2.a.k 1
702.2.a.l 1
702.2.a.m 1
702.2.a.n 1
702.2.a.o 1
702.2.a.p 1
702.2.b \(\chi_{702}(649, \cdot)\) 702.2.b.a 2 1
702.2.b.b 2
702.2.b.c 2
702.2.b.d 2
702.2.b.e 4
702.2.b.f 4
702.2.b.g 4
702.2.e \(\chi_{702}(235, \cdot)\) 702.2.e.a 2 2
702.2.e.b 4
702.2.e.c 4
702.2.e.d 6
702.2.e.e 8
702.2.f \(\chi_{702}(289, \cdot)\) 702.2.f.a 2 2
702.2.f.b 2
702.2.f.c 12
702.2.f.d 12
702.2.g \(\chi_{702}(451, \cdot)\) 702.2.g.a 2 2
702.2.g.b 2
702.2.g.c 12
702.2.g.d 12
702.2.h \(\chi_{702}(55, \cdot)\) 702.2.h.a 2 2
702.2.h.b 2
702.2.h.c 2
702.2.h.d 2
702.2.h.e 2
702.2.h.f 2
702.2.h.g 4
702.2.h.h 4
702.2.h.i 4
702.2.h.j 4
702.2.h.k 4
702.2.h.l 4
702.2.j \(\chi_{702}(161, \cdot)\) 702.2.j.a 16 2
702.2.j.b 24
702.2.l \(\chi_{702}(433, \cdot)\) 702.2.l.a 8 2
702.2.l.b 8
702.2.l.c 8
702.2.l.d 12
702.2.p \(\chi_{702}(361, \cdot)\) 702.2.p.a 28 2
702.2.s \(\chi_{702}(127, \cdot)\) 702.2.s.a 28 2
702.2.t \(\chi_{702}(181, \cdot)\) 702.2.t.a 28 2
702.2.w \(\chi_{702}(79, \cdot)\) 702.2.w.a 42 6
702.2.w.b 48
702.2.w.c 60
702.2.w.d 66
702.2.x \(\chi_{702}(61, \cdot)\) 702.2.x.a 126 6
702.2.x.b 126
702.2.y \(\chi_{702}(133, \cdot)\) 702.2.y.a 126 6
702.2.y.b 126
702.2.ba \(\chi_{702}(215, \cdot)\) 702.2.ba.a 16 4
702.2.ba.b 16
702.2.ba.c 16
702.2.ba.d 24
702.2.bb \(\chi_{702}(71, \cdot)\) 702.2.bb.a 56 4
702.2.bc \(\chi_{702}(305, \cdot)\) 702.2.bc.a 56 4
702.2.bg \(\chi_{702}(125, \cdot)\) 702.2.bg.a 56 4
702.2.bj \(\chi_{702}(43, \cdot)\) 702.2.bj.a 252 6
702.2.bk \(\chi_{702}(25, \cdot)\) 702.2.bk.a 252 6
702.2.bp \(\chi_{702}(121, \cdot)\) 702.2.bp.a 252 6
702.2.br \(\chi_{702}(41, \cdot)\) 702.2.br.a 504 12
702.2.bs \(\chi_{702}(5, \cdot)\) 702.2.bs.a 504 12
702.2.bv \(\chi_{702}(11, \cdot)\) 702.2.bv.a 504 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(702))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(702)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(702))\)\(^{\oplus 1}\)