↑

Properties

Label 65.6
Level 65
Weight 6
Dimension 728
Nonzero newspaces 12
Newform subspaces 18
Sturm bound 2016
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 18 \)
Sturm bound: \(2016\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(65))\).

Total New Old
Modular forms 888 796 92
Cusp forms 792 728 64
Eisenstein series 96 68 28

Trace form

\( 728 q - 16 q^{2} - 4 q^{3} + 92 q^{4} + 112 q^{5} - 548 q^{6} + 200 q^{7} - 924 q^{8} - 242 q^{9} + O(q^{10}) \) \( 728 q - 16 q^{2} - 4 q^{3} + 92 q^{4} + 112 q^{5} - 548 q^{6} + 200 q^{7} - 924 q^{8} - 242 q^{9} + 702 q^{10} + 320 q^{11} + 5536 q^{12} + 2846 q^{13} - 1320 q^{14} - 3646 q^{15} - 6532 q^{16} + 5738 q^{17} - 5980 q^{18} - 11228 q^{19} - 6274 q^{20} - 1080 q^{21} - 1160 q^{22} + 492 q^{23} + 37332 q^{24} - 4962 q^{25} + 33748 q^{26} + 26528 q^{27} + 55808 q^{28} + 34198 q^{29} - 28994 q^{30} - 81792 q^{31} - 168848 q^{32} - 83840 q^{33} - 48324 q^{34} + 1992 q^{35} + 170588 q^{36} + 71602 q^{37} + 99728 q^{38} + 159868 q^{39} + 119396 q^{40} + 24994 q^{41} - 129168 q^{42} - 166456 q^{43} - 269984 q^{44} - 151133 q^{45} - 158188 q^{46} - 61240 q^{47} - 53420 q^{48} + 46994 q^{49} - 18952 q^{50} + 291160 q^{51} + 411000 q^{52} + 152828 q^{53} + 347992 q^{54} + 287576 q^{55} + 232680 q^{56} + 30440 q^{57} - 164812 q^{58} - 29896 q^{59} - 431144 q^{60} - 505678 q^{61} - 1548 q^{62} - 134784 q^{63} - 265224 q^{64} - 324763 q^{65} - 573808 q^{66} - 226708 q^{67} - 1072304 q^{68} - 503856 q^{69} + 2916 q^{70} - 204044 q^{71} + 756960 q^{72} + 590112 q^{73} + 1671244 q^{74} + 1177310 q^{75} + 1138324 q^{76} + 626016 q^{77} + 1104464 q^{78} - 345296 q^{79} - 793600 q^{80} - 337634 q^{81} - 483220 q^{82} - 231720 q^{83} - 558000 q^{84} + 71739 q^{85} - 134752 q^{86} - 11788 q^{87} - 508512 q^{88} - 931944 q^{89} - 1025116 q^{90} - 939472 q^{91} - 227544 q^{92} - 829560 q^{93} + 385404 q^{94} + 180706 q^{95} + 1526168 q^{96} + 633088 q^{97} + 1114360 q^{98} + 821144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(65))\)

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
65.6.a \(\chi_{65}(1, \cdot)\) 65.6.a.a 1 1
65.6.a.b 3
65.6.a.c 4
65.6.a.d 6
65.6.a.e 6
65.6.b \(\chi_{65}(14, \cdot)\) 65.6.b.a 30 1
65.6.c \(\chi_{65}(51, \cdot)\) 65.6.c.a 8 1
65.6.c.b 14
65.6.d \(\chi_{65}(64, \cdot)\) 65.6.d.a 32 1
65.6.e \(\chi_{65}(16, \cdot)\) 65.6.e.a 24 2
65.6.e.b 24
65.6.f \(\chi_{65}(18, \cdot)\) 65.6.f.a 66 2
65.6.k \(\chi_{65}(8, \cdot)\) 65.6.k.a 66 2
65.6.l \(\chi_{65}(4, \cdot)\) 65.6.l.a 64 2
65.6.m \(\chi_{65}(36, \cdot)\) 65.6.m.a 48 2
65.6.n \(\chi_{65}(9, \cdot)\) 65.6.n.a 68 2
65.6.o \(\chi_{65}(2, \cdot)\) 65.6.o.a 132 4
65.6.t \(\chi_{65}(7, \cdot)\) 65.6.t.a 132 4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(65))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(65)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 1}\)