Properties

Label 72.1
Level 72
Weight 1
Dimension 2
Nonzero newspaces 1
Newforms 1
Sturm bound 288
Trace bound 0

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(72))\).

Total New Old
Modular forms 50 11 39
Cusp forms 2 2 0
Eisenstein series 48 9 39

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{24} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut -\mathstrut q^{36} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut -\mathstrut q^{54} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut +\mathstrut q^{59} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut +\mathstrut q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{72} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut +\mathstrut q^{76} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 2q^{83} \) \(\mathstrut +\mathstrut q^{86} \) \(\mathstrut +\mathstrut q^{88} \) \(\mathstrut +\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
72.1.b \(\chi_{72}(19, \cdot)\) None 0 1
72.1.e \(\chi_{72}(17, \cdot)\) None 0 1
72.1.g \(\chi_{72}(55, \cdot)\) None 0 1
72.1.h \(\chi_{72}(53, \cdot)\) None 0 1
72.1.j \(\chi_{72}(5, \cdot)\) None 0 2
72.1.k \(\chi_{72}(7, \cdot)\) None 0 2
72.1.m \(\chi_{72}(41, \cdot)\) None 0 2
72.1.p \(\chi_{72}(43, \cdot)\) 72.1.p.a 2 2