Properties

Label 175.2
Level 175
Weight 2
Dimension 959
Nonzero newspaces 12
Newforms 32
Sturm bound 4800
Trace bound 2

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Defining parameters

Level: \( N \) = \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newforms: \( 32 \)
Sturm bound: \(4800\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(175))\).

Total New Old
Modular forms 1368 1163 205
Cusp forms 1033 959 74
Eisenstein series 335 204 131

Trace form

\(959q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 28q^{3} \) \(\mathstrut -\mathstrut 37q^{4} \) \(\mathstrut -\mathstrut 38q^{5} \) \(\mathstrut -\mathstrut 60q^{6} \) \(\mathstrut -\mathstrut 41q^{7} \) \(\mathstrut -\mathstrut 97q^{8} \) \(\mathstrut -\mathstrut 55q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(959q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 28q^{3} \) \(\mathstrut -\mathstrut 37q^{4} \) \(\mathstrut -\mathstrut 38q^{5} \) \(\mathstrut -\mathstrut 60q^{6} \) \(\mathstrut -\mathstrut 41q^{7} \) \(\mathstrut -\mathstrut 97q^{8} \) \(\mathstrut -\mathstrut 55q^{9} \) \(\mathstrut -\mathstrut 58q^{10} \) \(\mathstrut -\mathstrut 60q^{11} \) \(\mathstrut -\mathstrut 100q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 71q^{14} \) \(\mathstrut -\mathstrut 116q^{15} \) \(\mathstrut -\mathstrut 85q^{16} \) \(\mathstrut -\mathstrut 50q^{17} \) \(\mathstrut -\mathstrut 83q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 28q^{20} \) \(\mathstrut -\mathstrut 82q^{21} \) \(\mathstrut -\mathstrut 80q^{22} \) \(\mathstrut -\mathstrut 48q^{23} \) \(\mathstrut +\mathstrut 40q^{24} \) \(\mathstrut -\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 102q^{26} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 54q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut -\mathstrut 32q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 32q^{35} \) \(\mathstrut -\mathstrut 53q^{36} \) \(\mathstrut -\mathstrut 48q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 62q^{41} \) \(\mathstrut +\mathstrut 38q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 32q^{44} \) \(\mathstrut +\mathstrut 38q^{45} \) \(\mathstrut -\mathstrut 72q^{46} \) \(\mathstrut -\mathstrut 56q^{47} \) \(\mathstrut +\mathstrut 56q^{48} \) \(\mathstrut -\mathstrut 105q^{49} \) \(\mathstrut -\mathstrut 46q^{50} \) \(\mathstrut -\mathstrut 160q^{51} \) \(\mathstrut +\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 88q^{53} \) \(\mathstrut +\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 44q^{55} \) \(\mathstrut -\mathstrut 79q^{56} \) \(\mathstrut -\mathstrut 36q^{57} \) \(\mathstrut +\mathstrut 46q^{58} \) \(\mathstrut +\mathstrut 92q^{60} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 132q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 75q^{64} \) \(\mathstrut +\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 48q^{66} \) \(\mathstrut +\mathstrut 52q^{67} \) \(\mathstrut +\mathstrut 158q^{68} \) \(\mathstrut +\mathstrut 52q^{69} \) \(\mathstrut +\mathstrut 102q^{70} \) \(\mathstrut -\mathstrut 124q^{71} \) \(\mathstrut +\mathstrut 147q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 126q^{74} \) \(\mathstrut +\mathstrut 28q^{75} \) \(\mathstrut +\mathstrut 28q^{76} \) \(\mathstrut +\mathstrut 18q^{77} \) \(\mathstrut -\mathstrut 8q^{78} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 98q^{80} \) \(\mathstrut -\mathstrut 91q^{81} \) \(\mathstrut +\mathstrut 86q^{82} \) \(\mathstrut +\mathstrut 48q^{83} \) \(\mathstrut +\mathstrut 90q^{84} \) \(\mathstrut +\mathstrut 22q^{85} \) \(\mathstrut -\mathstrut 36q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 180q^{88} \) \(\mathstrut +\mathstrut 84q^{89} \) \(\mathstrut +\mathstrut 170q^{90} \) \(\mathstrut -\mathstrut 56q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 28q^{93} \) \(\mathstrut +\mathstrut 64q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 114q^{97} \) \(\mathstrut +\mathstrut 125q^{98} \) \(\mathstrut -\mathstrut 68q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)

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
175.2.a \(\chi_{175}(1, \cdot)\) 175.2.a.a 1 1
175.2.a.b 1
175.2.a.c 1
175.2.a.d 2
175.2.a.e 2
175.2.a.f 2
175.2.b \(\chi_{175}(99, \cdot)\) 175.2.b.a 2 1
175.2.b.b 4
175.2.b.c 4
175.2.e \(\chi_{175}(51, \cdot)\) 175.2.e.a 2 2
175.2.e.b 2
175.2.e.c 4
175.2.e.d 6
175.2.e.e 6
175.2.f \(\chi_{175}(118, \cdot)\) 175.2.f.a 4 2
175.2.f.b 4
175.2.f.c 4
175.2.f.d 8
175.2.h \(\chi_{175}(36, \cdot)\) 175.2.h.a 4 4
175.2.h.b 28
175.2.h.c 32
175.2.k \(\chi_{175}(74, \cdot)\) 175.2.k.a 8 2
175.2.k.b 12
175.2.n \(\chi_{175}(29, \cdot)\) 175.2.n.a 56 4
175.2.o \(\chi_{175}(68, \cdot)\) 175.2.o.a 4 4
175.2.o.b 4
175.2.o.c 8
175.2.o.d 24
175.2.q \(\chi_{175}(11, \cdot)\) 175.2.q.a 144 8
175.2.s \(\chi_{175}(13, \cdot)\) 175.2.s.a 144 8
175.2.t \(\chi_{175}(4, \cdot)\) 175.2.t.a 144 8
175.2.x \(\chi_{175}(3, \cdot)\) 175.2.x.a 288 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(175)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)