Properties

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

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Defining parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 18 \)
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

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

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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(65)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 1}\)