Properties

Label 162.2
Level 162
Weight 2
Dimension 192
Nonzero newspaces 4
Newforms 12
Sturm bound 2916
Trace bound 1

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Defining parameters

Level: \( N \) = \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 12 \)
Sturm bound: \(2916\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(162))\).

Total New Old
Modular forms 837 192 645
Cusp forms 622 192 430
Eisenstein series 215 0 215

Trace form

\(192q \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(192q \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 9q^{18} \) \(\mathstrut -\mathstrut 18q^{19} \) \(\mathstrut -\mathstrut 30q^{20} \) \(\mathstrut -\mathstrut 54q^{21} \) \(\mathstrut -\mathstrut 21q^{22} \) \(\mathstrut -\mathstrut 78q^{23} \) \(\mathstrut -\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 90q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut -\mathstrut 84q^{29} \) \(\mathstrut -\mathstrut 54q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 54q^{33} \) \(\mathstrut -\mathstrut 15q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut -\mathstrut 18q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 3q^{41} \) \(\mathstrut +\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 54q^{45} \) \(\mathstrut +\mathstrut 12q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 12q^{49} \) \(\mathstrut +\mathstrut 36q^{50} \) \(\mathstrut -\mathstrut 63q^{51} \) \(\mathstrut +\mathstrut 12q^{52} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 36q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 69q^{59} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 3q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 72q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut +\mathstrut 30q^{68} \) \(\mathstrut +\mathstrut 126q^{69} \) \(\mathstrut -\mathstrut 24q^{70} \) \(\mathstrut +\mathstrut 120q^{71} \) \(\mathstrut +\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 42q^{73} \) \(\mathstrut +\mathstrut 114q^{74} \) \(\mathstrut +\mathstrut 180q^{75} \) \(\mathstrut -\mathstrut 15q^{76} \) \(\mathstrut +\mathstrut 246q^{77} \) \(\mathstrut +\mathstrut 144q^{78} \) \(\mathstrut -\mathstrut 60q^{79} \) \(\mathstrut +\mathstrut 24q^{80} \) \(\mathstrut +\mathstrut 144q^{81} \) \(\mathstrut +\mathstrut 6q^{82} \) \(\mathstrut +\mathstrut 144q^{83} \) \(\mathstrut +\mathstrut 36q^{84} \) \(\mathstrut -\mathstrut 36q^{85} \) \(\mathstrut +\mathstrut 117q^{86} \) \(\mathstrut +\mathstrut 288q^{87} \) \(\mathstrut -\mathstrut 21q^{88} \) \(\mathstrut +\mathstrut 174q^{89} \) \(\mathstrut +\mathstrut 144q^{90} \) \(\mathstrut +\mathstrut 30q^{91} \) \(\mathstrut +\mathstrut 66q^{92} \) \(\mathstrut +\mathstrut 126q^{93} \) \(\mathstrut -\mathstrut 18q^{94} \) \(\mathstrut +\mathstrut 84q^{95} \) \(\mathstrut +\mathstrut 18q^{96} \) \(\mathstrut -\mathstrut 15q^{97} \) \(\mathstrut +\mathstrut 87q^{98} \) \(\mathstrut +\mathstrut 18q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)

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
162.2.a \(\chi_{162}(1, \cdot)\) 162.2.a.a 1 1
162.2.a.b 1
162.2.a.c 1
162.2.a.d 1
162.2.c \(\chi_{162}(55, \cdot)\) 162.2.c.a 2 2
162.2.c.b 2
162.2.c.c 2
162.2.c.d 2
162.2.e \(\chi_{162}(19, \cdot)\) 162.2.e.a 6 6
162.2.e.b 12
162.2.g \(\chi_{162}(7, \cdot)\) 162.2.g.a 72 18
162.2.g.b 90

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(162)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)