Properties

Label 105.2
Level 105
Weight 2
Dimension 227
Nonzero newspaces 12
Newforms 25
Sturm bound 1536
Trace bound 4

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Defining parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newforms: \( 25 \)
Sturm bound: \(1536\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(105))\).

Total New Old
Modular forms 480 283 197
Cusp forms 289 227 62
Eisenstein series 191 56 135

Trace form

\(227q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut 19q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 35q^{6} \) \(\mathstrut -\mathstrut 21q^{7} \) \(\mathstrut -\mathstrut 27q^{8} \) \(\mathstrut -\mathstrut 21q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(227q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut 19q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 35q^{6} \) \(\mathstrut -\mathstrut 21q^{7} \) \(\mathstrut -\mathstrut 27q^{8} \) \(\mathstrut -\mathstrut 21q^{9} \) \(\mathstrut -\mathstrut 43q^{10} \) \(\mathstrut -\mathstrut 16q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 34q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 21q^{15} \) \(\mathstrut -\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 27q^{20} \) \(\mathstrut -\mathstrut 25q^{21} \) \(\mathstrut -\mathstrut 68q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 21q^{24} \) \(\mathstrut -\mathstrut 37q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 10q^{29} \) \(\mathstrut +\mathstrut 37q^{30} \) \(\mathstrut -\mathstrut 44q^{31} \) \(\mathstrut +\mathstrut 85q^{32} \) \(\mathstrut +\mathstrut 16q^{33} \) \(\mathstrut +\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 26q^{37} \) \(\mathstrut +\mathstrut 56q^{38} \) \(\mathstrut +\mathstrut 30q^{39} \) \(\mathstrut +\mathstrut 45q^{40} \) \(\mathstrut +\mathstrut 22q^{41} \) \(\mathstrut +\mathstrut 57q^{42} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 72q^{46} \) \(\mathstrut -\mathstrut 52q^{47} \) \(\mathstrut +\mathstrut 45q^{48} \) \(\mathstrut -\mathstrut 57q^{49} \) \(\mathstrut -\mathstrut 55q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 18q^{52} \) \(\mathstrut -\mathstrut 22q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut -\mathstrut 3q^{56} \) \(\mathstrut -\mathstrut 36q^{57} \) \(\mathstrut +\mathstrut 86q^{58} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 65q^{60} \) \(\mathstrut +\mathstrut 38q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 85q^{64} \) \(\mathstrut +\mathstrut 72q^{65} \) \(\mathstrut +\mathstrut 92q^{66} \) \(\mathstrut +\mathstrut 80q^{67} \) \(\mathstrut +\mathstrut 130q^{68} \) \(\mathstrut +\mathstrut 72q^{69} \) \(\mathstrut +\mathstrut 249q^{70} \) \(\mathstrut +\mathstrut 64q^{71} \) \(\mathstrut +\mathstrut 57q^{72} \) \(\mathstrut +\mathstrut 134q^{73} \) \(\mathstrut +\mathstrut 154q^{74} \) \(\mathstrut +\mathstrut 91q^{75} \) \(\mathstrut +\mathstrut 108q^{76} \) \(\mathstrut +\mathstrut 84q^{77} \) \(\mathstrut +\mathstrut 70q^{78} \) \(\mathstrut +\mathstrut 92q^{79} \) \(\mathstrut +\mathstrut 69q^{80} \) \(\mathstrut -\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 74q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 31q^{84} \) \(\mathstrut -\mathstrut 58q^{85} \) \(\mathstrut -\mathstrut 16q^{86} \) \(\mathstrut -\mathstrut 46q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 18q^{89} \) \(\mathstrut -\mathstrut 115q^{90} \) \(\mathstrut -\mathstrut 158q^{91} \) \(\mathstrut -\mathstrut 168q^{92} \) \(\mathstrut -\mathstrut 80q^{93} \) \(\mathstrut -\mathstrut 176q^{94} \) \(\mathstrut -\mathstrut 102q^{95} \) \(\mathstrut -\mathstrut 271q^{96} \) \(\mathstrut -\mathstrut 138q^{97} \) \(\mathstrut -\mathstrut 167q^{98} \) \(\mathstrut -\mathstrut 124q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)

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
105.2.a \(\chi_{105}(1, \cdot)\) 105.2.a.a 1 1
105.2.a.b 2
105.2.b \(\chi_{105}(41, \cdot)\) 105.2.b.a 2 1
105.2.b.b 2
105.2.b.c 4
105.2.b.d 4
105.2.d \(\chi_{105}(64, \cdot)\) 105.2.d.a 2 1
105.2.d.b 6
105.2.g \(\chi_{105}(104, \cdot)\) 105.2.g.a 4 1
105.2.g.b 4
105.2.g.c 4
105.2.i \(\chi_{105}(16, \cdot)\) 105.2.i.a 2 2
105.2.i.b 2
105.2.i.c 4
105.2.i.d 4
105.2.j \(\chi_{105}(8, \cdot)\) 105.2.j.a 24 2
105.2.m \(\chi_{105}(13, \cdot)\) 105.2.m.a 16 2
105.2.p \(\chi_{105}(59, \cdot)\) 105.2.p.a 24 2
105.2.q \(\chi_{105}(4, \cdot)\) 105.2.q.a 16 2
105.2.s \(\chi_{105}(26, \cdot)\) 105.2.s.a 2 2
105.2.s.b 2
105.2.s.c 8
105.2.s.d 8
105.2.u \(\chi_{105}(52, \cdot)\) 105.2.u.a 32 4
105.2.x \(\chi_{105}(2, \cdot)\) 105.2.x.a 48 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(105)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)