Properties

Label 55.1
Level 55
Weight 1
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 240
Trace bound 0

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Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(55))\).

Total New Old
Modular forms 41 27 14
Cusp forms 1 1 0
Eisenstein series 40 26 14

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

\( q - q^{4} - q^{5} + q^{9} + O(q^{10}) \) \( q - q^{4} - q^{5} + q^{9} - q^{11} + q^{16} + q^{20} + q^{25} - 2 q^{31} - q^{36} + q^{44} - q^{45} - q^{49} + q^{55} + 2 q^{59} - q^{64} + 2 q^{71} - q^{80} + q^{81} - 2 q^{89} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)

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
55.1.c \(\chi_{55}(21, \cdot)\) None 0 1
55.1.d \(\chi_{55}(54, \cdot)\) 55.1.d.a 1 1
55.1.f \(\chi_{55}(12, \cdot)\) None 0 2
55.1.h \(\chi_{55}(19, \cdot)\) None 0 4
55.1.i \(\chi_{55}(6, \cdot)\) None 0 4
55.1.k \(\chi_{55}(3, \cdot)\) None 0 8