Properties

Label 440.2
Level 440
Weight 2
Dimension 2812
Nonzero newspaces 18
Newform subspaces 50
Sturm bound 23040
Trace bound 6

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Defining parameters

Level: \( N \) = \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 50 \)
Sturm bound: \(23040\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(440))\).

Total New Old
Modular forms 6240 3028 3212
Cusp forms 5281 2812 2469
Eisenstein series 959 216 743

Trace form

\( 2812 q - 12 q^{2} - 12 q^{3} - 12 q^{4} + 2 q^{5} - 44 q^{6} - 4 q^{7} - 12 q^{8} - 14 q^{9} + O(q^{10}) \) \( 2812 q - 12 q^{2} - 12 q^{3} - 12 q^{4} + 2 q^{5} - 44 q^{6} - 4 q^{7} - 12 q^{8} - 14 q^{9} - 22 q^{10} - 48 q^{11} - 56 q^{12} + 4 q^{13} - 36 q^{14} - 28 q^{15} - 76 q^{16} - 8 q^{17} - 68 q^{18} - 14 q^{19} - 62 q^{20} + 24 q^{21} - 36 q^{22} - 20 q^{23} - 68 q^{24} - 14 q^{25} - 76 q^{26} - 6 q^{27} - 4 q^{28} + 32 q^{29} - 60 q^{30} - 40 q^{31} + 8 q^{32} - 62 q^{33} - 48 q^{34} - 76 q^{35} - 140 q^{36} - 12 q^{37} - 72 q^{38} - 156 q^{39} - 12 q^{40} - 144 q^{41} - 192 q^{42} - 140 q^{43} - 144 q^{44} - 28 q^{45} - 136 q^{46} - 128 q^{47} - 224 q^{48} - 114 q^{49} - 132 q^{50} - 186 q^{51} - 160 q^{52} + 28 q^{53} - 228 q^{54} - 68 q^{55} - 296 q^{56} - 22 q^{57} - 128 q^{58} + 10 q^{59} - 160 q^{60} + 84 q^{61} - 132 q^{62} + 16 q^{63} - 84 q^{64} - 48 q^{65} - 76 q^{66} + 80 q^{67} - 60 q^{68} + 64 q^{69} + 40 q^{70} + 28 q^{71} + 104 q^{72} - 112 q^{73} + 120 q^{74} + 52 q^{75} + 100 q^{76} + 36 q^{77} + 328 q^{78} - 20 q^{79} + 128 q^{80} - 176 q^{81} + 252 q^{82} - 90 q^{83} + 284 q^{84} - 64 q^{85} + 44 q^{86} - 144 q^{87} + 300 q^{88} - 168 q^{89} + 118 q^{90} - 288 q^{91} + 172 q^{92} - 180 q^{93} + 156 q^{94} - 166 q^{95} - 16 q^{96} - 162 q^{97} + 176 q^{98} - 316 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)

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
440.2.a \(\chi_{440}(1, \cdot)\) 440.2.a.a 1 1
440.2.a.b 1
440.2.a.c 1
440.2.a.d 1
440.2.a.e 2
440.2.a.f 2
440.2.a.g 2
440.2.b \(\chi_{440}(89, \cdot)\) 440.2.b.a 2 1
440.2.b.b 2
440.2.b.c 2
440.2.b.d 8
440.2.c \(\chi_{440}(219, \cdot)\) 440.2.c.a 4 1
440.2.c.b 8
440.2.c.c 56
440.2.f \(\chi_{440}(351, \cdot)\) None 0 1
440.2.g \(\chi_{440}(221, \cdot)\) 440.2.g.a 4 1
440.2.g.b 12
440.2.g.c 24
440.2.l \(\chi_{440}(309, \cdot)\) 440.2.l.a 2 1
440.2.l.b 2
440.2.l.c 56
440.2.m \(\chi_{440}(439, \cdot)\) None 0 1
440.2.p \(\chi_{440}(131, \cdot)\) 440.2.p.a 48 1
440.2.r \(\chi_{440}(67, \cdot)\) 440.2.r.a 2 2
440.2.r.b 2
440.2.r.c 2
440.2.r.d 2
440.2.r.e 4
440.2.r.f 4
440.2.r.g 48
440.2.r.h 56
440.2.t \(\chi_{440}(197, \cdot)\) 440.2.t.a 4 2
440.2.t.b 4
440.2.t.c 128
440.2.v \(\chi_{440}(153, \cdot)\) 440.2.v.a 4 2
440.2.v.b 32
440.2.x \(\chi_{440}(23, \cdot)\) None 0 2
440.2.y \(\chi_{440}(81, \cdot)\) 440.2.y.a 8 4
440.2.y.b 12
440.2.y.c 12
440.2.y.d 16
440.2.z \(\chi_{440}(51, \cdot)\) 440.2.z.a 192 4
440.2.bc \(\chi_{440}(39, \cdot)\) None 0 4
440.2.bd \(\chi_{440}(69, \cdot)\) 440.2.bd.a 272 4
440.2.bi \(\chi_{440}(141, \cdot)\) 440.2.bi.a 8 4
440.2.bi.b 8
440.2.bi.c 176
440.2.bj \(\chi_{440}(151, \cdot)\) None 0 4
440.2.bm \(\chi_{440}(19, \cdot)\) 440.2.bm.a 8 4
440.2.bm.b 8
440.2.bm.c 256
440.2.bn \(\chi_{440}(9, \cdot)\) 440.2.bn.a 72 4
440.2.bo \(\chi_{440}(17, \cdot)\) 440.2.bo.a 144 8
440.2.bq \(\chi_{440}(47, \cdot)\) None 0 8
440.2.bs \(\chi_{440}(3, \cdot)\) 440.2.bs.a 544 8
440.2.bu \(\chi_{440}(13, \cdot)\) 440.2.bu.a 544 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(440))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(440)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 2}\)