Properties

Label 164.2
Level 164
Weight 2
Dimension 450
Nonzero newspaces 8
Newforms 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: \( 8 \)
Newforms: \( 10 \)
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

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

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 the 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

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