Properties

Label 72.2
Level 72
Weight 2
Dimension 55
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 576
Trace bound 2

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(576\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(72))\).

Total New Old
Modular forms 192 73 119
Cusp forms 97 55 42
Eisenstein series 95 18 77

Trace form

\( 55 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + 4 q^{5} - 8 q^{6} - 2 q^{7} - 14 q^{8} - 9 q^{9} - 24 q^{10} - 17 q^{11} - 14 q^{12} - 2 q^{13} - 14 q^{14} - 24 q^{15} - 10 q^{16} - 20 q^{17} - 22 q^{19} + 10 q^{20}+ \cdots + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.2.a \(\chi_{72}(1, \cdot)\) 72.2.a.a 1 1
72.2.c \(\chi_{72}(71, \cdot)\) None 0 1
72.2.d \(\chi_{72}(37, \cdot)\) 72.2.d.a 2 1
72.2.d.b 2
72.2.f \(\chi_{72}(35, \cdot)\) 72.2.f.a 4 1
72.2.i \(\chi_{72}(25, \cdot)\) 72.2.i.a 2 2
72.2.i.b 4
72.2.l \(\chi_{72}(11, \cdot)\) 72.2.l.a 4 2
72.2.l.b 16
72.2.n \(\chi_{72}(13, \cdot)\) 72.2.n.a 4 2
72.2.n.b 16
72.2.o \(\chi_{72}(23, \cdot)\) None 0 2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)