Properties

Label 65.2
Level 65
Weight 2
Dimension 117
Nonzero newspaces 12
Newforms 18
Sturm bound 672
Trace bound 3

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Defining parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newforms: \( 18 \)
Sturm bound: \(672\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(65))\).

Total New Old
Modular forms 216 185 31
Cusp forms 121 117 4
Eisenstein series 95 68 27

Trace form

\(117q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 16q^{3} \) \(\mathstrut -\mathstrut 19q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 48q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(117q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 16q^{3} \) \(\mathstrut -\mathstrut 19q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 48q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 36q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut -\mathstrut 24q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut -\mathstrut 27q^{16} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 48q^{24} \) \(\mathstrut -\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 15q^{26} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 32q^{28} \) \(\mathstrut +\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 42q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 57q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut +\mathstrut 30q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 41q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut +\mathstrut 21q^{40} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut +\mathstrut 72q^{42} \) \(\mathstrut +\mathstrut 36q^{43} \) \(\mathstrut +\mathstrut 60q^{44} \) \(\mathstrut +\mathstrut 44q^{45} \) \(\mathstrut +\mathstrut 60q^{46} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut -\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 47q^{49} \) \(\mathstrut +\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 21q^{52} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 72q^{54} \) \(\mathstrut -\mathstrut 36q^{55} \) \(\mathstrut -\mathstrut 72q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 60q^{58} \) \(\mathstrut -\mathstrut 60q^{59} \) \(\mathstrut -\mathstrut 172q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 88q^{63} \) \(\mathstrut -\mathstrut 97q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 144q^{66} \) \(\mathstrut -\mathstrut 64q^{67} \) \(\mathstrut -\mathstrut 72q^{68} \) \(\mathstrut -\mathstrut 120q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 36q^{71} \) \(\mathstrut -\mathstrut 123q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut -\mathstrut 30q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut +\mathstrut 36q^{78} \) \(\mathstrut -\mathstrut 32q^{79} \) \(\mathstrut +\mathstrut 62q^{80} \) \(\mathstrut +\mathstrut 3q^{81} \) \(\mathstrut +\mathstrut 72q^{82} \) \(\mathstrut +\mathstrut 60q^{83} \) \(\mathstrut +\mathstrut 56q^{84} \) \(\mathstrut +\mathstrut 57q^{85} \) \(\mathstrut +\mathstrut 84q^{86} \) \(\mathstrut +\mathstrut 108q^{87} \) \(\mathstrut +\mathstrut 156q^{88} \) \(\mathstrut +\mathstrut 90q^{89} \) \(\mathstrut +\mathstrut 165q^{90} \) \(\mathstrut +\mathstrut 56q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 128q^{93} \) \(\mathstrut +\mathstrut 132q^{94} \) \(\mathstrut +\mathstrut 70q^{95} \) \(\mathstrut +\mathstrut 204q^{96} \) \(\mathstrut +\mathstrut 50q^{97} \) \(\mathstrut +\mathstrut 105q^{98} \) \(\mathstrut +\mathstrut 132q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)

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
65.2.a \(\chi_{65}(1, \cdot)\) 65.2.a.a 1 1
65.2.a.b 2
65.2.a.c 2
65.2.b \(\chi_{65}(14, \cdot)\) 65.2.b.a 6 1
65.2.c \(\chi_{65}(51, \cdot)\) 65.2.c.a 6 1
65.2.d \(\chi_{65}(64, \cdot)\) 65.2.d.a 2 1
65.2.d.b 2
65.2.e \(\chi_{65}(16, \cdot)\) 65.2.e.a 4 2
65.2.e.b 4
65.2.f \(\chi_{65}(18, \cdot)\) 65.2.f.a 2 2
65.2.f.b 8
65.2.k \(\chi_{65}(8, \cdot)\) 65.2.k.a 2 2
65.2.k.b 8
65.2.l \(\chi_{65}(4, \cdot)\) 65.2.l.a 8 2
65.2.m \(\chi_{65}(36, \cdot)\) 65.2.m.a 8 2
65.2.n \(\chi_{65}(9, \cdot)\) 65.2.n.a 12 2
65.2.o \(\chi_{65}(2, \cdot)\) 65.2.o.a 20 4
65.2.t \(\chi_{65}(7, \cdot)\) 65.2.t.a 20 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(65))\) into lower level spaces

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