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Properties

Label 65.3
Level 65
Weight 3
Dimension 272
Nonzero newspaces 8
Newform subspaces 8
Sturm bound 1008
Trace bound 5

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Defining parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 8 \)
Sturm bound: \(1008\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(65))\).

Total New Old
Modular forms 384 336 48
Cusp forms 288 272 16
Eisenstein series 96 64 32

Trace form

\( 272 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 18 q^{5} - 36 q^{6} - 32 q^{7} - 84 q^{8} - 60 q^{9} + O(q^{10}) \) \( 272 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 18 q^{5} - 36 q^{6} - 32 q^{7} - 84 q^{8} - 60 q^{9} - 48 q^{10} - 48 q^{11} - 24 q^{12} + 12 q^{13} + 24 q^{14} + 18 q^{15} + 124 q^{16} - 84 q^{18} - 44 q^{19} - 66 q^{20} - 192 q^{21} - 192 q^{22} - 60 q^{23} - 156 q^{24} - 24 q^{25} + 24 q^{26} + 120 q^{27} + 56 q^{28} - 108 q^{29} + 30 q^{30} - 88 q^{31} - 24 q^{32} + 192 q^{33} + 228 q^{34} + 12 q^{35} + 60 q^{36} + 32 q^{37} - 24 q^{38} - 156 q^{39} - 204 q^{40} - 312 q^{41} - 264 q^{42} - 384 q^{43} + 144 q^{44} - 78 q^{45} - 252 q^{46} + 120 q^{47} + 612 q^{48} + 120 q^{49} + 318 q^{50} + 576 q^{51} + 824 q^{52} + 384 q^{53} + 1080 q^{54} + 660 q^{55} + 1272 q^{56} + 936 q^{57} + 984 q^{58} + 552 q^{59} + 1236 q^{60} + 936 q^{61} + 252 q^{62} + 168 q^{63} - 228 q^{65} - 864 q^{66} - 380 q^{67} - 1776 q^{68} - 1008 q^{69} - 1020 q^{70} - 780 q^{71} - 2376 q^{72} - 788 q^{73} - 1440 q^{74} - 1242 q^{75} - 1964 q^{76} - 960 q^{77} - 1368 q^{78} - 816 q^{79} - 1140 q^{80} - 420 q^{81} - 288 q^{82} + 456 q^{83} - 528 q^{84} + 24 q^{85} + 360 q^{86} - 420 q^{87} + 384 q^{88} - 204 q^{89} - 24 q^{90} - 464 q^{91} + 1176 q^{92} - 144 q^{93} + 828 q^{94} + 54 q^{95} - 768 q^{96} - 244 q^{97} - 444 q^{98} - 744 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(65))\)

We only show spaces with odd 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
65.3.g \(\chi_{65}(34, \cdot)\) 65.3.g.a 24 2
65.3.h \(\chi_{65}(12, \cdot)\) 65.3.h.a 24 2
65.3.i \(\chi_{65}(27, \cdot)\) 65.3.i.a 24 2
65.3.j \(\chi_{65}(21, \cdot)\) 65.3.j.a 16 2
65.3.p \(\chi_{65}(6, \cdot)\) 65.3.p.a 40 4
65.3.q \(\chi_{65}(3, \cdot)\) 65.3.q.a 48 4
65.3.r \(\chi_{65}(17, \cdot)\) 65.3.r.a 48 4
65.3.s \(\chi_{65}(19, \cdot)\) 65.3.s.a 48 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(65))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(65)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 1}\)