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Properties

Label 385.2
Level 385
Weight 2
Dimension 4711
Nonzero newspaces 24
Newform subspaces 54
Sturm bound 23040
Trace bound 5

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Defining parameters

Level: \( N \) = \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 54 \)
Sturm bound: \(23040\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(385))\).

Total New Old
Modular forms 6240 5247 993
Cusp forms 5281 4711 570
Eisenstein series 959 536 423

Trace form

\( 4711 q - 19 q^{2} - 20 q^{3} - 23 q^{4} - 45 q^{5} - 104 q^{6} - 49 q^{7} - 107 q^{8} - 69 q^{9} + O(q^{10}) \) \( 4711 q - 19 q^{2} - 20 q^{3} - 23 q^{4} - 45 q^{5} - 104 q^{6} - 49 q^{7} - 107 q^{8} - 69 q^{9} - 93 q^{10} - 117 q^{11} - 164 q^{12} - 50 q^{13} - 95 q^{14} - 178 q^{15} - 223 q^{16} - 94 q^{17} - 175 q^{18} - 96 q^{19} - 169 q^{20} - 204 q^{21} - 199 q^{22} - 140 q^{23} - 200 q^{24} - 121 q^{25} - 246 q^{26} - 104 q^{27} - 131 q^{28} - 134 q^{29} - 130 q^{30} - 136 q^{31} - 135 q^{32} - 132 q^{33} - 150 q^{34} - 93 q^{35} - 463 q^{36} - 102 q^{37} - 200 q^{38} - 172 q^{39} - 37 q^{40} - 246 q^{41} - 188 q^{42} - 148 q^{43} - 107 q^{44} - 161 q^{45} - 196 q^{46} - 60 q^{47} - 136 q^{48} - 133 q^{49} - 199 q^{50} - 244 q^{51} - 38 q^{52} - 170 q^{53} - 132 q^{54} - 33 q^{55} - 411 q^{56} - 176 q^{57} + 66 q^{58} - 60 q^{59} + 122 q^{60} + 50 q^{61} - 36 q^{62} + 87 q^{63} + 149 q^{64} + 42 q^{65} + 176 q^{66} + 48 q^{67} + 190 q^{68} + 124 q^{69} + 187 q^{70} - 220 q^{71} + 397 q^{72} + 22 q^{73} - 86 q^{74} + 20 q^{75} + 196 q^{76} - 29 q^{77} - 152 q^{78} - 64 q^{79} - 73 q^{80} - 29 q^{81} - 82 q^{82} - 164 q^{83} + 316 q^{84} - 258 q^{85} - 160 q^{86} - 176 q^{87} - 155 q^{88} - 166 q^{89} + 99 q^{90} - 198 q^{91} - 152 q^{92} - 76 q^{93} - 188 q^{94} - 64 q^{95} + 32 q^{96} - 130 q^{97} - 59 q^{98} - 153 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)

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
385.2.a \(\chi_{385}(1, \cdot)\) 385.2.a.a 1 1
385.2.a.b 1
385.2.a.c 2
385.2.a.d 2
385.2.a.e 3
385.2.a.f 3
385.2.a.g 3
385.2.a.h 4
385.2.b \(\chi_{385}(309, \cdot)\) 385.2.b.a 2 1
385.2.b.b 2
385.2.b.c 12
385.2.b.d 16
385.2.c \(\chi_{385}(76, \cdot)\) 385.2.c.a 32 1
385.2.h \(\chi_{385}(384, \cdot)\) 385.2.h.a 4 1
385.2.h.b 8
385.2.h.c 32
385.2.i \(\chi_{385}(221, \cdot)\) 385.2.i.a 8 2
385.2.i.b 12
385.2.i.c 16
385.2.i.d 20
385.2.j \(\chi_{385}(188, \cdot)\) 385.2.j.a 4 2
385.2.j.b 4
385.2.j.c 32
385.2.j.d 40
385.2.k \(\chi_{385}(43, \cdot)\) 385.2.k.a 72 2
385.2.n \(\chi_{385}(36, \cdot)\) 385.2.n.a 4 4
385.2.n.b 4
385.2.n.c 8
385.2.n.d 16
385.2.n.e 28
385.2.n.f 36
385.2.o \(\chi_{385}(54, \cdot)\) 385.2.o.a 16 2
385.2.o.b 72
385.2.t \(\chi_{385}(144, \cdot)\) 385.2.t.a 4 2
385.2.t.b 36
385.2.t.c 40
385.2.u \(\chi_{385}(131, \cdot)\) 385.2.u.a 64 2
385.2.v \(\chi_{385}(139, \cdot)\) 385.2.v.a 8 4
385.2.v.b 8
385.2.v.c 160
385.2.ba \(\chi_{385}(6, \cdot)\) 385.2.ba.a 128 4
385.2.bb \(\chi_{385}(64, \cdot)\) 385.2.bb.a 144 4
385.2.bc \(\chi_{385}(32, \cdot)\) 385.2.bc.a 176 4
385.2.bd \(\chi_{385}(12, \cdot)\) 385.2.bd.a 80 4
385.2.bd.b 80
385.2.bg \(\chi_{385}(16, \cdot)\) 385.2.bg.a 128 8
385.2.bg.b 128
385.2.bj \(\chi_{385}(8, \cdot)\) 385.2.bj.a 288 8
385.2.bk \(\chi_{385}(27, \cdot)\) 385.2.bk.a 352 8
385.2.bl \(\chi_{385}(61, \cdot)\) 385.2.bl.a 256 8
385.2.bm \(\chi_{385}(4, \cdot)\) 385.2.bm.a 352 8
385.2.br \(\chi_{385}(19, \cdot)\) 385.2.br.a 352 8
385.2.bu \(\chi_{385}(3, \cdot)\) 385.2.bu.a 704 16
385.2.bv \(\chi_{385}(2, \cdot)\) 385.2.bv.a 704 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(385))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(385)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)