Properties

Label 144.1
Level 144
Weight 1
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 1152
Trace bound 0

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(1152\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(144))\).

Total New Old
Modular forms 117 21 96
Cusp forms 5 1 4
Eisenstein series 112 20 92

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\(q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.1.b \(\chi_{144}(55, \cdot)\) None 0 1
144.1.e \(\chi_{144}(17, \cdot)\) None 0 1
144.1.g \(\chi_{144}(127, \cdot)\) 144.1.g.a 1 1
144.1.h \(\chi_{144}(89, \cdot)\) None 0 1
144.1.j \(\chi_{144}(53, \cdot)\) None 0 2
144.1.m \(\chi_{144}(19, \cdot)\) None 0 2
144.1.n \(\chi_{144}(41, \cdot)\) None 0 2
144.1.o \(\chi_{144}(31, \cdot)\) None 0 2
144.1.q \(\chi_{144}(65, \cdot)\) None 0 2
144.1.t \(\chi_{144}(7, \cdot)\) None 0 2
144.1.v \(\chi_{144}(43, \cdot)\) None 0 4
144.1.w \(\chi_{144}(5, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)