Properties

Label 162.2
Level 162
Weight 2
Dimension 192
Nonzero newspaces 4
Newform subspaces 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: \( 4 \)
Newform subspaces: \( 12 \)
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

\( 192 q + 6 q^{5} + 6 q^{7} + 3 q^{8} + 6 q^{10} + 15 q^{11} + 12 q^{13} + 6 q^{14} + 12 q^{17} - 9 q^{18} - 18 q^{19} - 30 q^{20} - 54 q^{21} - 21 q^{22} - 78 q^{23} - 36 q^{25} - 90 q^{26} - 54 q^{27} - 24 q^{28}+ \cdots + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(162)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)