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Properties

Label 364.2
Level 364
Weight 2
Dimension 2118
Nonzero newspaces 30
Newform subspaces 51
Sturm bound 16128
Trace bound 9

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Defining parameters

Level: \( N \) = \( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 51 \)
Sturm bound: \(16128\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(364))\).

Total New Old
Modular forms 4392 2334 2058
Cusp forms 3673 2118 1555
Eisenstein series 719 216 503

Trace form

\( 2118 q - 18 q^{2} + 2 q^{3} - 18 q^{4} - 30 q^{5} - 24 q^{6} + 10 q^{7} - 54 q^{8} - 24 q^{9} + O(q^{10}) \) \( 2118 q - 18 q^{2} + 2 q^{3} - 18 q^{4} - 30 q^{5} - 24 q^{6} + 10 q^{7} - 54 q^{8} - 24 q^{9} - 36 q^{10} + 6 q^{11} - 60 q^{12} - 28 q^{13} - 78 q^{14} + 12 q^{15} - 42 q^{16} - 24 q^{17} - 66 q^{18} - 10 q^{19} - 72 q^{20} - 92 q^{21} - 84 q^{22} - 18 q^{23} - 96 q^{24} - 106 q^{25} - 72 q^{26} - 52 q^{27} - 6 q^{28} - 126 q^{29} - 108 q^{30} - 10 q^{31} - 78 q^{32} - 78 q^{33} - 72 q^{34} - 12 q^{35} - 78 q^{36} - 40 q^{37} - 72 q^{38} + 42 q^{39} - 24 q^{40} - 90 q^{41} - 36 q^{42} + 12 q^{43} - 90 q^{45} + 72 q^{46} - 6 q^{47} + 72 q^{48} - 90 q^{49} + 18 q^{50} + 6 q^{51} + 84 q^{52} - 102 q^{53} + 96 q^{54} + 24 q^{55} + 6 q^{56} - 136 q^{57} + 84 q^{58} + 30 q^{59} + 60 q^{60} - 80 q^{61} + 22 q^{63} - 90 q^{64} - 144 q^{65} - 108 q^{66} - 22 q^{67} - 180 q^{68} - 48 q^{69} - 84 q^{70} - 72 q^{71} - 150 q^{72} - 178 q^{73} - 168 q^{74} - 108 q^{75} - 144 q^{76} - 234 q^{77} - 312 q^{78} - 146 q^{79} - 204 q^{80} - 366 q^{81} - 168 q^{82} - 240 q^{83} - 72 q^{84} - 414 q^{85} - 96 q^{86} - 252 q^{87} - 144 q^{88} - 270 q^{89} - 146 q^{91} - 156 q^{92} - 202 q^{93} + 60 q^{94} - 150 q^{95} + 204 q^{96} - 112 q^{97} + 54 q^{98} - 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)

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
364.2.a \(\chi_{364}(1, \cdot)\) 364.2.a.a 1 1
364.2.a.b 1
364.2.a.c 2
364.2.a.d 2
364.2.f \(\chi_{364}(27, \cdot)\) 364.2.f.a 4 1
364.2.f.b 16
364.2.f.c 28
364.2.g \(\chi_{364}(337, \cdot)\) 364.2.g.a 8 1
364.2.h \(\chi_{364}(363, \cdot)\) 364.2.h.a 4 1
364.2.h.b 48
364.2.i \(\chi_{364}(165, \cdot)\) 364.2.i.a 18 2
364.2.j \(\chi_{364}(53, \cdot)\) 364.2.j.a 2 2
364.2.j.b 2
364.2.j.c 2
364.2.j.d 2
364.2.j.e 8
364.2.k \(\chi_{364}(29, \cdot)\) 364.2.k.a 2 2
364.2.k.b 2
364.2.k.c 4
364.2.k.d 4
364.2.l \(\chi_{364}(9, \cdot)\) 364.2.l.a 18 2
364.2.m \(\chi_{364}(99, \cdot)\) 364.2.m.a 84 2
364.2.n \(\chi_{364}(125, \cdot)\) 364.2.n.a 16 2
364.2.u \(\chi_{364}(225, \cdot)\) 364.2.u.a 16 2
364.2.v \(\chi_{364}(55, \cdot)\) 364.2.v.a 4 2
364.2.v.b 4
364.2.v.c 8
364.2.v.d 8
364.2.v.e 8
364.2.v.f 72
364.2.w \(\chi_{364}(75, \cdot)\) 364.2.w.a 104 2
364.2.x \(\chi_{364}(103, \cdot)\) 364.2.x.a 8 2
364.2.x.b 96
364.2.y \(\chi_{364}(25, \cdot)\) 364.2.y.a 8 2
364.2.y.b 12
364.2.z \(\chi_{364}(131, \cdot)\) 364.2.z.a 96 2
364.2.ba \(\chi_{364}(87, \cdot)\) 364.2.ba.a 104 2
364.2.bb \(\chi_{364}(205, \cdot)\) 364.2.bb.a 18 2
364.2.bc \(\chi_{364}(251, \cdot)\) 364.2.bc.a 104 2
364.2.bp \(\chi_{364}(283, \cdot)\) 364.2.bp.a 104 2
364.2.bq \(\chi_{364}(121, \cdot)\) 364.2.bq.a 18 2
364.2.br \(\chi_{364}(3, \cdot)\) 364.2.br.a 104 2
364.2.bs \(\chi_{364}(33, \cdot)\) 364.2.bs.a 36 4
364.2.bt \(\chi_{364}(11, \cdot)\) 364.2.bt.a 208 4
364.2.ca \(\chi_{364}(123, \cdot)\) 364.2.ca.a 208 4
364.2.cb \(\chi_{364}(41, \cdot)\) 364.2.cb.a 40 4
364.2.cc \(\chi_{364}(5, \cdot)\) 364.2.cc.a 40 4
364.2.cd \(\chi_{364}(15, \cdot)\) 364.2.cd.a 8 4
364.2.cd.b 160
364.2.ce \(\chi_{364}(135, \cdot)\) 364.2.ce.a 208 4
364.2.cf \(\chi_{364}(45, \cdot)\) 364.2.cf.a 36 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(364))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(364)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 1}\)