↑

Properties

Label 174.2
Level 174
Weight 2
Dimension 211
Nonzero newspaces 6
Newform subspaces 17
Sturm bound 3360
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 174 = 2 \cdot 3 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 17 \)
Sturm bound: \(3360\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(174))\).

Total New Old
Modular forms 952 211 741
Cusp forms 729 211 518
Eisenstein series 223 0 223

Trace form

\( 211 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 211 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + q^{16} + 18 q^{17} + q^{18} + 20 q^{19} - 8 q^{20} - 48 q^{21} - 44 q^{22} - 32 q^{23} - 27 q^{24} - 81 q^{25} - 56 q^{26} - 83 q^{27} + 8 q^{28} - 83 q^{29} - 78 q^{30} - 80 q^{31} + q^{32} - 72 q^{33} - 52 q^{34} - 64 q^{35} - 27 q^{36} - 18 q^{37} - 36 q^{38} - 42 q^{39} - 8 q^{40} + 42 q^{41} + 8 q^{42} + 44 q^{43} + 12 q^{44} - 8 q^{45} + 24 q^{46} - 8 q^{47} + q^{48} - 55 q^{49} + 31 q^{50} - 38 q^{51} + 14 q^{52} - 72 q^{53} + q^{54} - 152 q^{55} + 8 q^{56} - 36 q^{57} + 29 q^{58} + 4 q^{59} + 6 q^{60} - 50 q^{61} + 32 q^{62} - 20 q^{63} + q^{64} - 42 q^{65} + 12 q^{66} - 44 q^{67} + 18 q^{68} - 32 q^{69} + 48 q^{70} + 16 q^{71} + q^{72} + 4 q^{73} + 38 q^{74} + 171 q^{75} + 20 q^{76} + 96 q^{77} + 126 q^{78} + 80 q^{79} + 6 q^{80} + 225 q^{81} + 42 q^{82} + 84 q^{83} + 92 q^{84} + 108 q^{85} + 44 q^{86} + 169 q^{87} + 12 q^{88} + 90 q^{89} + 146 q^{90} + 112 q^{91} + 24 q^{92} + 144 q^{93} + 48 q^{94} + 120 q^{95} + q^{96} + 84 q^{97} + 57 q^{98} + 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)

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
174.2.a \(\chi_{174}(1, \cdot)\) 174.2.a.a 1 1
174.2.a.b 1
174.2.a.c 1
174.2.a.d 1
174.2.a.e 1
174.2.d \(\chi_{174}(115, \cdot)\) 174.2.d.a 2 1
174.2.d.b 4
174.2.f \(\chi_{174}(17, \cdot)\) 174.2.f.a 4 2
174.2.f.b 4
174.2.f.c 4
174.2.f.d 8
174.2.g \(\chi_{174}(7, \cdot)\) 174.2.g.a 6 6
174.2.g.b 6
174.2.g.c 12
174.2.h \(\chi_{174}(13, \cdot)\) 174.2.h.a 12 6
174.2.h.b 24
174.2.k \(\chi_{174}(11, \cdot)\) 174.2.k.a 120 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(174))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(174)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)