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Properties

Label 170.2
Level 170
Weight 2
Dimension 265
Nonzero newspaces 10
Newform subspaces 30
Sturm bound 3456
Trace bound 10

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Defining parameters

Level: \( N \) = \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 30 \)
Sturm bound: \(3456\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(170))\).

Total New Old
Modular forms 992 265 727
Cusp forms 737 265 472
Eisenstein series 255 0 255

Trace form

\( 265 q + q^{2} + 4 q^{3} + q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + O(q^{10}) \) \( 265 q + q^{2} + 4 q^{3} + q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} - 3 q^{10} - 20 q^{11} - 12 q^{12} - 18 q^{13} - 24 q^{14} - 44 q^{15} - 7 q^{16} - 15 q^{17} - 51 q^{18} - 12 q^{19} - 3 q^{20} - 64 q^{21} - 20 q^{22} - 8 q^{23} - 12 q^{24} - 35 q^{25} + 6 q^{26} - 8 q^{27} + 8 q^{28} - 10 q^{29} + 4 q^{30} - 32 q^{31} + q^{32} - 16 q^{33} + 17 q^{34} - 24 q^{35} + 13 q^{36} - 26 q^{37} + 4 q^{38} - 72 q^{39} + q^{40} - 94 q^{41} - 64 q^{42} - 68 q^{43} - 52 q^{44} - 71 q^{45} - 40 q^{46} - 112 q^{47} + 4 q^{48} - 71 q^{49} - 15 q^{50} - 60 q^{51} - 50 q^{52} - 82 q^{53} - 72 q^{54} - 68 q^{55} + 8 q^{56} - 96 q^{57} - 34 q^{58} - 100 q^{59} - 28 q^{60} - 34 q^{61} - 64 q^{62} - 88 q^{63} + q^{64} - 22 q^{65} + 32 q^{66} + 36 q^{67} + 25 q^{68} + 96 q^{69} + 104 q^{70} + 104 q^{71} + 53 q^{72} + 226 q^{73} + 110 q^{74} + 148 q^{75} + 20 q^{76} + 192 q^{77} + 184 q^{78} + 176 q^{79} + 49 q^{80} + 297 q^{81} + 178 q^{82} + 132 q^{83} + 96 q^{84} + 269 q^{85} + 108 q^{86} + 216 q^{87} + 76 q^{88} + 90 q^{89} + 217 q^{90} + 176 q^{91} + 56 q^{92} + 128 q^{93} + 176 q^{94} + 132 q^{95} + 4 q^{96} + 162 q^{97} + 129 q^{98} + 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)

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
170.2.a \(\chi_{170}(1, \cdot)\) 170.2.a.a 1 1
170.2.a.b 1
170.2.a.c 1
170.2.a.d 1
170.2.a.e 1
170.2.a.f 2
170.2.b \(\chi_{170}(101, \cdot)\) 170.2.b.a 2 1
170.2.b.b 2
170.2.b.c 2
170.2.c \(\chi_{170}(69, \cdot)\) 170.2.c.a 2 1
170.2.c.b 6
170.2.d \(\chi_{170}(169, \cdot)\) 170.2.d.a 2 1
170.2.d.b 2
170.2.d.c 4
170.2.g \(\chi_{170}(89, \cdot)\) 170.2.g.a 2 2
170.2.g.b 2
170.2.g.c 2
170.2.g.d 2
170.2.g.e 4
170.2.g.f 4
170.2.h \(\chi_{170}(21, \cdot)\) 170.2.h.a 4 2
170.2.h.b 8
170.2.k \(\chi_{170}(111, \cdot)\) 170.2.k.a 8 4
170.2.k.b 16
170.2.n \(\chi_{170}(9, \cdot)\) 170.2.n.a 20 4
170.2.n.b 20
170.2.o \(\chi_{170}(3, \cdot)\) 170.2.o.a 32 8
170.2.o.b 40
170.2.r \(\chi_{170}(23, \cdot)\) 170.2.r.a 32 8
170.2.r.b 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(170))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(170)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 1}\)