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Properties

Label 40.2
Level 40
Weight 2
Dimension 19
Nonzero newspaces 5
Newform subspaces 5
Sturm bound 192
Trace bound 2

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Defining parameters

Level: \( N \) = \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 5 \)
Sturm bound: \(192\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(40))\).

Total New Old
Modular forms 72 31 41
Cusp forms 25 19 6
Eisenstein series 47 12 35

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)

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
40.2.a \(\chi_{40}(1, \cdot)\) 40.2.a.a 1 1
40.2.c \(\chi_{40}(9, \cdot)\) 40.2.c.a 2 1
40.2.d \(\chi_{40}(21, \cdot)\) 40.2.d.a 4 1
40.2.f \(\chi_{40}(29, \cdot)\) 40.2.f.a 4 1
40.2.j \(\chi_{40}(7, \cdot)\) None 0 2
40.2.k \(\chi_{40}(3, \cdot)\) 40.2.k.a 8 2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(40))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(40)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 1}\)