Properties

Label 192.1
Level 192
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 2048
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(2048\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(192))\).

Total New Old
Modular forms 146 24 122
Cusp forms 2 2 0
Eisenstein series 144 22 122

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

\( 2q - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{9} - 2q^{25} - 2q^{49} + 4q^{57} + 4q^{73} + 2q^{81} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.1.b \(\chi_{192}(31, \cdot)\) None 0 1
192.1.e \(\chi_{192}(65, \cdot)\) None 0 1
192.1.g \(\chi_{192}(127, \cdot)\) None 0 1
192.1.h \(\chi_{192}(161, \cdot)\) 192.1.h.a 2 1
192.1.i \(\chi_{192}(17, \cdot)\) None 0 2
192.1.l \(\chi_{192}(79, \cdot)\) None 0 2
192.1.m \(\chi_{192}(7, \cdot)\) None 0 4
192.1.p \(\chi_{192}(41, \cdot)\) None 0 4
192.1.q \(\chi_{192}(5, \cdot)\) None 0 8
192.1.t \(\chi_{192}(19, \cdot)\) None 0 8