Properties

Label 70.3
Level 70
Weight 3
Dimension 84
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 864
Trace bound 4

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Defining parameters

Level: \( N \) = \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 9 \)
Sturm bound: \(864\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(70))\).

Total New Old
Modular forms 336 84 252
Cusp forms 240 84 156
Eisenstein series 96 0 96

Trace form

\( 84 q + 4 q^{2} + 20 q^{3} + 8 q^{4} + 6 q^{5} - 16 q^{6} - 20 q^{7} - 8 q^{8} + O(q^{10}) \) \( 84 q + 4 q^{2} + 20 q^{3} + 8 q^{4} + 6 q^{5} - 16 q^{6} - 20 q^{7} - 8 q^{8} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 12 q^{13} + 72 q^{14} - 4 q^{15} + 32 q^{16} + 32 q^{17} + 44 q^{18} - 12 q^{19} - 40 q^{20} - 92 q^{21} - 80 q^{22} - 52 q^{23} - 48 q^{24} - 70 q^{25} - 216 q^{26} - 424 q^{27} - 96 q^{28} - 336 q^{29} - 276 q^{30} - 268 q^{31} - 16 q^{32} - 4 q^{33} + 94 q^{35} + 104 q^{36} + 352 q^{37} + 296 q^{38} + 576 q^{39} + 88 q^{40} + 368 q^{41} + 416 q^{42} + 616 q^{43} + 168 q^{44} + 628 q^{45} + 200 q^{46} + 36 q^{47} - 32 q^{48} + 40 q^{49} - 4 q^{50} + 4 q^{51} + 120 q^{52} - 56 q^{53} + 72 q^{54} - 336 q^{55} - 112 q^{56} - 760 q^{57} - 208 q^{58} - 324 q^{59} + 44 q^{60} - 300 q^{61} + 208 q^{62} - 140 q^{63} - 64 q^{64} - 144 q^{65} + 416 q^{66} - 324 q^{67} - 64 q^{68} - 44 q^{70} + 256 q^{71} + 88 q^{72} - 64 q^{73} - 192 q^{74} + 94 q^{75} - 160 q^{76} + 356 q^{77} - 240 q^{78} + 740 q^{79} - 24 q^{80} + 544 q^{81} + 208 q^{82} + 600 q^{83} - 24 q^{84} + 664 q^{85} - 816 q^{86} - 184 q^{87} - 272 q^{88} - 1044 q^{89} - 1324 q^{90} - 1320 q^{91} - 320 q^{92} - 1156 q^{93} - 936 q^{94} - 1298 q^{95} - 32 q^{96} - 756 q^{97} - 444 q^{98} - 1248 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
70.3.b \(\chi_{70}(41, \cdot)\) 70.3.b.a 8 1
70.3.d \(\chi_{70}(69, \cdot)\) 70.3.d.a 8 1
70.3.f \(\chi_{70}(43, \cdot)\) 70.3.f.a 4 2
70.3.f.b 8
70.3.h \(\chi_{70}(19, \cdot)\) 70.3.h.a 16 2
70.3.j \(\chi_{70}(31, \cdot)\) 70.3.j.a 8 2
70.3.l \(\chi_{70}(23, \cdot)\) 70.3.l.a 8 4
70.3.l.b 8
70.3.l.c 16

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(70))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(70)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)