Properties

Label 170.2
Level 170
Weight 2
Dimension 265
Nonzero newspaces 10
Newforms 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: \( 10 \)
Newforms: \( 30 \)
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

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

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 the 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

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