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Properties

Label 164.2
Level 164
Weight 2
Dimension 450
Nonzero newspaces 8
Newform subspaces 10
Sturm bound 3360
Trace bound 3

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Defining parameters

Level: \( N \) = \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 10 \)
Sturm bound: \(3360\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(164))\).

Total New Old
Modular forms 940 530 410
Cusp forms 741 450 291
Eisenstein series 199 80 119

Trace form

\( 450 q - 20 q^{2} - 20 q^{4} - 40 q^{5} - 20 q^{6} - 20 q^{8} - 40 q^{9} + O(q^{10}) \) \( 450 q - 20 q^{2} - 20 q^{4} - 40 q^{5} - 20 q^{6} - 20 q^{8} - 40 q^{9} - 20 q^{10} - 20 q^{12} - 40 q^{13} - 20 q^{14} - 20 q^{16} - 40 q^{17} - 20 q^{18} - 20 q^{20} - 40 q^{21} - 20 q^{22} - 20 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{28} - 40 q^{29} - 20 q^{30} - 20 q^{31} - 20 q^{32} - 100 q^{33} - 20 q^{34} - 40 q^{35} - 20 q^{36} - 100 q^{37} - 20 q^{38} - 80 q^{39} - 60 q^{41} - 40 q^{42} - 20 q^{43} - 20 q^{44} - 120 q^{45} - 20 q^{46} - 60 q^{47} - 20 q^{48} - 80 q^{49} - 20 q^{50} - 60 q^{51} - 20 q^{52} - 60 q^{53} - 20 q^{54} - 20 q^{56} - 40 q^{57} - 20 q^{58} - 20 q^{60} - 40 q^{61} - 20 q^{62} - 20 q^{64} - 30 q^{65} + 60 q^{66} + 60 q^{67} + 80 q^{68} + 40 q^{69} + 180 q^{70} + 80 q^{71} + 160 q^{72} + 40 q^{73} + 100 q^{74} + 160 q^{75} + 280 q^{76} + 40 q^{77} + 180 q^{78} + 80 q^{79} + 180 q^{80} + 170 q^{81} + 220 q^{82} + 80 q^{83} + 220 q^{84} + 130 q^{85} + 180 q^{86} + 80 q^{87} + 180 q^{88} + 40 q^{89} + 280 q^{90} + 160 q^{91} + 100 q^{92} + 40 q^{93} + 160 q^{94} + 80 q^{95} + 180 q^{96} + 40 q^{97} + 80 q^{98} + 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)

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
164.2.a \(\chi_{164}(1, \cdot)\) 164.2.a.a 4 1
164.2.b \(\chi_{164}(81, \cdot)\) 164.2.b.a 4 1
164.2.f \(\chi_{164}(9, \cdot)\) 164.2.f.a 6 2
164.2.g \(\chi_{164}(37, \cdot)\) 164.2.g.a 16 4
164.2.i \(\chi_{164}(3, \cdot)\) 164.2.i.a 4 4
164.2.i.b 72
164.2.k \(\chi_{164}(25, \cdot)\) 164.2.k.a 16 4
164.2.m \(\chi_{164}(5, \cdot)\) 164.2.m.a 24 8
164.2.o \(\chi_{164}(7, \cdot)\) 164.2.o.a 16 16
164.2.o.b 288

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(164))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(164)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 2}\)