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Properties

Label 44.1
Level 44
Weight 1
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 120
Trace bound 0

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Defining parameters

Level: \( N \) = \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(44))\).

Total New Old
Modular forms 26 9 17
Cusp forms 1 1 0
Eisenstein series 25 8 17

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

\( q - q^{3} - q^{5} + O(q^{10}) \) \( q - q^{3} - q^{5} + q^{11} + q^{15} - q^{23} + q^{27} - q^{31} - q^{33} - q^{37} + 2 q^{47} + q^{49} + 2 q^{53} - q^{55} - q^{59} - q^{67} + q^{69} - q^{71} - q^{81} - q^{89} + q^{93} - q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
44.1.b \(\chi_{44}(23, \cdot)\) None 0 1
44.1.d \(\chi_{44}(21, \cdot)\) 44.1.d.a 1 1
44.1.f \(\chi_{44}(13, \cdot)\) None 0 4
44.1.h \(\chi_{44}(3, \cdot)\) None 0 4