Properties

Label 130.2
Level 130
Weight 2
Dimension 155
Nonzero newspaces 12
Newforms 30
Sturm bound 2016
Trace bound 9

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Defining parameters

Level: \( N \) = \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newforms: \( 30 \)
Sturm bound: \(2016\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(130))\).

Total New Old
Modular forms 600 155 445
Cusp forms 409 155 254
Eisenstein series 191 0 191

Trace form

\(155q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut -\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(155q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut -\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 14q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 35q^{13} \) \(\mathstrut -\mathstrut 16q^{14} \) \(\mathstrut -\mathstrut 20q^{15} \) \(\mathstrut -\mathstrut 7q^{16} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 32q^{27} \) \(\mathstrut -\mathstrut 48q^{29} \) \(\mathstrut -\mathstrut 20q^{30} \) \(\mathstrut -\mathstrut 48q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut -\mathstrut 72q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 64q^{35} \) \(\mathstrut -\mathstrut 35q^{36} \) \(\mathstrut -\mathstrut 24q^{37} \) \(\mathstrut -\mathstrut 52q^{38} \) \(\mathstrut -\mathstrut 52q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut 60q^{41} \) \(\mathstrut -\mathstrut 40q^{42} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 36q^{44} \) \(\mathstrut -\mathstrut 62q^{45} \) \(\mathstrut -\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut +\mathstrut 4q^{48} \) \(\mathstrut -\mathstrut 7q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 24q^{51} \) \(\mathstrut +\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 78q^{53} \) \(\mathstrut +\mathstrut 112q^{54} \) \(\mathstrut +\mathstrut 96q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut +\mathstrut 192q^{57} \) \(\mathstrut +\mathstrut 84q^{58} \) \(\mathstrut +\mathstrut 108q^{59} \) \(\mathstrut +\mathstrut 76q^{60} \) \(\mathstrut +\mathstrut 80q^{61} \) \(\mathstrut +\mathstrut 104q^{62} \) \(\mathstrut +\mathstrut 192q^{63} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 118q^{65} \) \(\mathstrut +\mathstrut 144q^{66} \) \(\mathstrut +\mathstrut 108q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 192q^{69} \) \(\mathstrut +\mathstrut 116q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut 61q^{72} \) \(\mathstrut +\mathstrut 42q^{73} \) \(\mathstrut +\mathstrut 68q^{74} \) \(\mathstrut +\mathstrut 116q^{75} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 76q^{78} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 48q^{82} \) \(\mathstrut -\mathstrut 108q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 105q^{85} \) \(\mathstrut -\mathstrut 4q^{86} \) \(\mathstrut -\mathstrut 120q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 102q^{89} \) \(\mathstrut -\mathstrut 47q^{90} \) \(\mathstrut -\mathstrut 48q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 96q^{93} \) \(\mathstrut -\mathstrut 72q^{94} \) \(\mathstrut -\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 39q^{98} \) \(\mathstrut -\mathstrut 60q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)

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
130.2.a \(\chi_{130}(1, \cdot)\) 130.2.a.a 1 1
130.2.a.b 1
130.2.a.c 1
130.2.b \(\chi_{130}(79, \cdot)\) 130.2.b.a 6 1
130.2.c \(\chi_{130}(129, \cdot)\) 130.2.c.a 4 1
130.2.c.b 4
130.2.d \(\chi_{130}(51, \cdot)\) 130.2.d.a 2 1
130.2.e \(\chi_{130}(61, \cdot)\) 130.2.e.a 2 2
130.2.e.b 2
130.2.e.c 4
130.2.e.d 4
130.2.g \(\chi_{130}(57, \cdot)\) 130.2.g.a 2 2
130.2.g.b 2
130.2.g.c 2
130.2.g.d 4
130.2.g.e 4
130.2.j \(\chi_{130}(47, \cdot)\) 130.2.j.a 2 2
130.2.j.b 2
130.2.j.c 2
130.2.j.d 4
130.2.j.e 4
130.2.l \(\chi_{130}(101, \cdot)\) 130.2.l.a 4 2
130.2.l.b 8
130.2.m \(\chi_{130}(49, \cdot)\) 130.2.m.a 8 2
130.2.m.b 8
130.2.n \(\chi_{130}(9, \cdot)\) 130.2.n.a 12 2
130.2.p \(\chi_{130}(7, \cdot)\) 130.2.p.a 12 4
130.2.p.b 16
130.2.s \(\chi_{130}(33, \cdot)\) 130.2.s.a 12 4
130.2.s.b 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(130))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(130)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)