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Properties

Label 220.2
Level 220
Weight 2
Dimension 704
Nonzero newspaces 12
Newform subspaces 26
Sturm bound 5760
Trace bound 4

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Defining parameters

Level: \( N \) = \( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 26 \)
Sturm bound: \(5760\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(220))\).

Total New Old
Modular forms 1640 808 832
Cusp forms 1241 704 537
Eisenstein series 399 104 295

Trace form

\( 704 q - 6 q^{2} + 4 q^{3} - 10 q^{4} - 20 q^{5} - 30 q^{6} + 6 q^{7} - 18 q^{8} - 2 q^{9} + O(q^{10}) \) \( 704 q - 6 q^{2} + 4 q^{3} - 10 q^{4} - 20 q^{5} - 30 q^{6} + 6 q^{7} - 18 q^{8} - 2 q^{9} - 32 q^{10} + 10 q^{11} - 20 q^{12} - 10 q^{13} - 20 q^{14} - 4 q^{15} - 54 q^{16} - 30 q^{17} - 48 q^{18} - 22 q^{19} - 32 q^{20} - 112 q^{21} - 70 q^{22} - 22 q^{23} - 70 q^{24} - 54 q^{25} - 88 q^{26} - 8 q^{27} - 60 q^{28} - 22 q^{29} - 20 q^{30} + 8 q^{31} - 36 q^{32} + 20 q^{34} + 19 q^{35} - 4 q^{36} - 56 q^{37} + 40 q^{38} - 2 q^{39} + 28 q^{40} - 70 q^{41} + 80 q^{42} + 60 q^{44} - 180 q^{45} + 20 q^{46} - 38 q^{47} + 100 q^{48} - 124 q^{49} + 48 q^{50} - 114 q^{51} + 8 q^{52} - 194 q^{53} - 90 q^{55} - 120 q^{56} - 186 q^{57} - 96 q^{58} - 124 q^{59} - 60 q^{60} - 182 q^{61} - 160 q^{62} - 104 q^{63} - 130 q^{64} - 110 q^{65} - 160 q^{66} - 94 q^{67} - 116 q^{68} - 106 q^{69} - 40 q^{70} - 16 q^{71} - 86 q^{72} + 30 q^{73} - 100 q^{74} + 34 q^{75} - 40 q^{76} - 50 q^{77} - 26 q^{79} - 32 q^{80} + 88 q^{81} + 18 q^{82} + 38 q^{83} + 80 q^{84} + 59 q^{85} + 70 q^{86} + 124 q^{87} + 150 q^{88} + 62 q^{89} + 198 q^{90} + 102 q^{91} + 80 q^{92} + 144 q^{93} + 180 q^{94} + 97 q^{95} + 240 q^{96} + 64 q^{97} + 172 q^{98} + 180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)

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
220.2.a \(\chi_{220}(1, \cdot)\) 220.2.a.a 1 1
220.2.a.b 1
220.2.b \(\chi_{220}(89, \cdot)\) 220.2.b.a 2 1
220.2.b.b 4
220.2.d \(\chi_{220}(131, \cdot)\) 220.2.d.a 2 1
220.2.d.b 2
220.2.d.c 8
220.2.d.d 12
220.2.g \(\chi_{220}(219, \cdot)\) 220.2.g.a 8 1
220.2.g.b 24
220.2.k \(\chi_{220}(153, \cdot)\) 220.2.k.a 4 2
220.2.k.b 8
220.2.l \(\chi_{220}(23, \cdot)\) 220.2.l.a 2 2
220.2.l.b 2
220.2.l.c 28
220.2.l.d 28
220.2.m \(\chi_{220}(81, \cdot)\) 220.2.m.a 8 4
220.2.m.b 8
220.2.o \(\chi_{220}(19, \cdot)\) 220.2.o.a 128 4
220.2.r \(\chi_{220}(51, \cdot)\) 220.2.r.a 8 4
220.2.r.b 8
220.2.r.c 32
220.2.r.d 48
220.2.t \(\chi_{220}(9, \cdot)\) 220.2.t.a 24 4
220.2.u \(\chi_{220}(13, \cdot)\) 220.2.u.a 48 8
220.2.v \(\chi_{220}(3, \cdot)\) 220.2.v.a 256 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(220))\) into lower level spaces

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