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Properties

Label 221.2
Level 221
Weight 2
Dimension 1811
Nonzero newspaces 20
Newform subspaces 45
Sturm bound 8064
Trace bound 8

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Defining parameters

Level: \( N \) = \( 221 = 13 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 45 \)
Sturm bound: \(8064\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(221))\).

Total New Old
Modular forms 2208 2143 65
Cusp forms 1825 1811 14
Eisenstein series 383 332 51

Trace form

\( 1811 q - 77 q^{2} - 80 q^{3} - 89 q^{4} - 86 q^{5} - 104 q^{6} - 88 q^{7} - 95 q^{8} - 91 q^{9} + O(q^{10}) \) \( 1811 q - 77 q^{2} - 80 q^{3} - 89 q^{4} - 86 q^{5} - 104 q^{6} - 88 q^{7} - 95 q^{8} - 91 q^{9} - 84 q^{10} - 76 q^{11} - 52 q^{12} - 71 q^{13} - 168 q^{14} - 68 q^{15} - 49 q^{16} - 84 q^{17} - 135 q^{18} - 72 q^{19} - 72 q^{20} - 64 q^{21} - 84 q^{22} - 100 q^{23} - 48 q^{24} - 63 q^{25} - 61 q^{26} - 152 q^{27} - 40 q^{28} - 64 q^{29} - 12 q^{30} - 48 q^{31} - 13 q^{32} - 48 q^{33} - 3 q^{34} - 144 q^{35} - 13 q^{36} - 84 q^{37} - 68 q^{38} - 72 q^{39} - 86 q^{40} - 16 q^{41} + 16 q^{42} - 28 q^{43} + 28 q^{44} - 48 q^{45} - 20 q^{46} - 48 q^{47} - 16 q^{48} - 59 q^{49} - 33 q^{50} - 72 q^{51} - 123 q^{52} - 130 q^{53} + 16 q^{54} - 24 q^{55} + 40 q^{56} + 32 q^{57} - 12 q^{58} - 36 q^{59} + 88 q^{60} - 12 q^{61} + 20 q^{62} + 56 q^{63} + 21 q^{64} - 64 q^{66} - 80 q^{67} + 4 q^{68} - 56 q^{69} + 48 q^{70} - 68 q^{71} + 111 q^{72} + 46 q^{73} + 4 q^{74} + 60 q^{75} + 32 q^{76} - 16 q^{77} + 116 q^{78} - 144 q^{79} + 116 q^{80} - 15 q^{81} - 8 q^{82} - 36 q^{83} + 64 q^{84} - 7 q^{85} - 68 q^{86} + 4 q^{87} + 60 q^{88} - 2 q^{89} + 130 q^{90} + 16 q^{91} + 16 q^{92} + 8 q^{93} + 108 q^{94} + 12 q^{95} + 196 q^{96} - 74 q^{97} + 51 q^{98} + 68 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(221))\)

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
221.2.a \(\chi_{221}(1, \cdot)\) 221.2.a.a 1 1
221.2.a.b 1
221.2.a.c 2
221.2.a.d 2
221.2.a.e 2
221.2.a.f 3
221.2.a.g 6
221.2.b \(\chi_{221}(220, \cdot)\) 221.2.b.a 4 1
221.2.b.b 4
221.2.b.c 6
221.2.b.d 6
221.2.c \(\chi_{221}(103, \cdot)\) 221.2.c.a 2 1
221.2.c.b 4
221.2.c.c 4
221.2.c.d 10
221.2.d \(\chi_{221}(118, \cdot)\) 221.2.d.a 2 1
221.2.d.b 4
221.2.d.c 6
221.2.d.d 6
221.2.e \(\chi_{221}(35, \cdot)\) 221.2.e.a 14 2
221.2.e.b 22
221.2.f \(\chi_{221}(157, \cdot)\) 221.2.f.a 4 2
221.2.f.b 4
221.2.f.c 4
221.2.f.d 8
221.2.f.e 16
221.2.k \(\chi_{221}(38, \cdot)\) 221.2.k.a 40 2
221.2.l \(\chi_{221}(16, \cdot)\) 221.2.l.a 36 2
221.2.m \(\chi_{221}(69, \cdot)\) 221.2.m.a 2 2
221.2.m.b 12
221.2.m.c 22
221.2.n \(\chi_{221}(101, \cdot)\) 221.2.n.a 40 2
221.2.p \(\chi_{221}(25, \cdot)\) 221.2.p.a 4 4
221.2.p.b 4
221.2.p.c 64
221.2.q \(\chi_{221}(53, \cdot)\) 221.2.q.a 32 4
221.2.q.b 40
221.2.s \(\chi_{221}(4, \cdot)\) 221.2.s.a 80 4
221.2.x \(\chi_{221}(55, \cdot)\) 221.2.x.a 72 4
221.2.z \(\chi_{221}(44, \cdot)\) 221.2.z.a 152 8
221.2.ba \(\chi_{221}(5, \cdot)\) 221.2.ba.a 152 8
221.2.bd \(\chi_{221}(36, \cdot)\) 221.2.bd.a 144 8
221.2.be \(\chi_{221}(9, \cdot)\) 221.2.be.a 160 8
221.2.bh \(\chi_{221}(6, \cdot)\) 221.2.bh.a 304 16
221.2.bi \(\chi_{221}(7, \cdot)\) 221.2.bi.a 304 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(221))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(221)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(221))\)\(^{\oplus 1}\)