Properties

Label 102.2
Level 102
Weight 2
Dimension 73
Nonzero newspaces 5
Newform subspaces 9
Sturm bound 1152
Trace bound 1

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Defining parameters

Level: \( N \) = \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1152\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(102))\).

Total New Old
Modular forms 352 73 279
Cusp forms 225 73 152
Eisenstein series 127 0 127

Trace form

\( 73 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} - 2 q^{10} - 20 q^{11} - 7 q^{12} - 18 q^{13} - 24 q^{14} - 42 q^{15} - 7 q^{16} - 15 q^{17} - 31 q^{18} - 12 q^{19} - 2 q^{20}+ \cdots + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)

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
102.2.a \(\chi_{102}(1, \cdot)\) 102.2.a.a 1 1
102.2.a.b 1
102.2.a.c 1
102.2.b \(\chi_{102}(67, \cdot)\) 102.2.b.a 2 1
102.2.f \(\chi_{102}(13, \cdot)\) 102.2.f.a 4 2
102.2.h \(\chi_{102}(19, \cdot)\) 102.2.h.a 8 4
102.2.h.b 8
102.2.i \(\chi_{102}(5, \cdot)\) 102.2.i.a 24 8
102.2.i.b 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(102))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(102)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)