Properties

Label 42.2
Level 42
Weight 2
Dimension 13
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 192
Trace bound 4

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Defining parameters

Level: \( N \) = \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(192\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(42))\).

Total New Old
Modular forms 72 13 59
Cusp forms 25 13 12
Eisenstein series 47 0 47

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)

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
42.2.a \(\chi_{42}(1, \cdot)\) 42.2.a.a 1 1
42.2.d \(\chi_{42}(41, \cdot)\) 42.2.d.a 4 1
42.2.e \(\chi_{42}(25, \cdot)\) 42.2.e.a 2 2
42.2.e.b 2
42.2.f \(\chi_{42}(5, \cdot)\) 42.2.f.a 4 2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(42))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(42)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 1}\)