Properties

Label 100.2
Level 100
Weight 2
Dimension 141
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 1200
Trace bound 1

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Defining parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(1200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(100))\).

Total New Old
Modular forms 370 181 189
Cusp forms 231 141 90
Eisenstein series 139 40 99

Trace form

\( 141 q - 6 q^{2} + 4 q^{3} - 10 q^{4} - 15 q^{5} - 18 q^{6} - 4 q^{7} - 18 q^{8} - 22 q^{9} - 16 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{14} - 2 q^{15} - 2 q^{16} - 30 q^{17} + 2 q^{18} - 12 q^{19} - 6 q^{20}+ \cdots + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)

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
100.2.a \(\chi_{100}(1, \cdot)\) 100.2.a.a 1 1
100.2.c \(\chi_{100}(49, \cdot)\) 100.2.c.a 2 1
100.2.e \(\chi_{100}(7, \cdot)\) 100.2.e.a 2 2
100.2.e.b 2
100.2.e.c 2
100.2.e.d 8
100.2.g \(\chi_{100}(21, \cdot)\) 100.2.g.a 12 4
100.2.i \(\chi_{100}(9, \cdot)\) 100.2.i.a 8 4
100.2.l \(\chi_{100}(3, \cdot)\) 100.2.l.a 8 8
100.2.l.b 96

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)