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Properties

Label 172.2
Level 172
Weight 2
Dimension 497
Nonzero newspaces 8
Newform subspaces 11
Sturm bound 3696
Trace bound 1

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Defining parameters

Level: \( N \) = \( 172 = 2^{2} \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 11 \)
Sturm bound: \(3696\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(172))\).

Total New Old
Modular forms 1029 581 448
Cusp forms 820 497 323
Eisenstein series 209 84 125

Trace form

\( 497 q - 21 q^{2} - 21 q^{4} - 42 q^{5} - 21 q^{6} - 21 q^{8} - 42 q^{9} + O(q^{10}) \) \( 497 q - 21 q^{2} - 21 q^{4} - 42 q^{5} - 21 q^{6} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 21 q^{12} - 42 q^{13} - 21 q^{14} - 21 q^{16} - 42 q^{17} - 21 q^{18} - 21 q^{20} - 42 q^{21} - 21 q^{22} - 21 q^{24} - 42 q^{25} - 21 q^{26} - 21 q^{28} - 42 q^{29} - 21 q^{30} - 7 q^{31} - 21 q^{32} - 84 q^{33} - 21 q^{34} - 42 q^{35} - 21 q^{36} - 84 q^{37} - 21 q^{38} - 49 q^{39} - 21 q^{40} - 63 q^{41} - 105 q^{43} - 42 q^{44} - 147 q^{45} - 21 q^{46} - 21 q^{47} - 21 q^{48} - 91 q^{49} - 21 q^{50} - 42 q^{51} - 21 q^{52} - 84 q^{53} - 21 q^{54} - 42 q^{55} - 21 q^{56} - 49 q^{57} - 21 q^{58} - 21 q^{60} - 42 q^{61} - 21 q^{62} - 21 q^{64} - 42 q^{65} - 21 q^{66} - 21 q^{68} + 63 q^{70} + 42 q^{71} + 189 q^{72} + 126 q^{74} + 147 q^{75} + 126 q^{76} + 84 q^{77} + 252 q^{78} + 84 q^{79} + 147 q^{80} + 126 q^{81} + 189 q^{82} + 84 q^{83} + 357 q^{84} + 84 q^{85} + 147 q^{86} + 210 q^{87} + 147 q^{88} + 42 q^{89} + 357 q^{90} + 84 q^{91} + 189 q^{92} + 126 q^{93} + 147 q^{94} + 84 q^{95} + 252 q^{96} + 84 q^{97} + 126 q^{98} + 147 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(172))\)

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
172.2.a \(\chi_{172}(1, \cdot)\) 172.2.a.a 1 1
172.2.a.b 2
172.2.d \(\chi_{172}(171, \cdot)\) 172.2.d.a 20 1
172.2.e \(\chi_{172}(49, \cdot)\) 172.2.e.a 8 2
172.2.f \(\chi_{172}(7, \cdot)\) 172.2.f.a 8 2
172.2.f.b 32
172.2.i \(\chi_{172}(21, \cdot)\) 172.2.i.a 6 6
172.2.i.b 12
172.2.j \(\chi_{172}(27, \cdot)\) 172.2.j.a 120 6
172.2.m \(\chi_{172}(9, \cdot)\) 172.2.m.a 48 12
172.2.p \(\chi_{172}(3, \cdot)\) 172.2.p.a 240 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(172))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(172)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 2}\)