Properties

Label 147.1
Level 147
Weight 1
Dimension 6
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1568
Trace bound 0

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Defining parameters

Level: \( N \) = \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(1568\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(147))\).

Total New Old
Modular forms 126 55 71
Cusp forms 6 6 0
Eisenstein series 120 49 71

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q - q^{3} - q^{4} - q^{7} - q^{9} + O(q^{10}) \) \( 6q - q^{3} - q^{4} - q^{7} - q^{9} - q^{12} - 2q^{13} - q^{16} - 2q^{19} - q^{21} - q^{25} - q^{27} - q^{28} - 2q^{31} - q^{36} + 5q^{37} + 5q^{39} - 2q^{43} + 6q^{48} - q^{49} + 5q^{52} - 2q^{57} + 5q^{61} + 6q^{63} - q^{64} - 2q^{67} - 2q^{73} - q^{75} - 2q^{76} - 2q^{79} - q^{81} - q^{84} - 2q^{91} - 2q^{93} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.1.b \(\chi_{147}(50, \cdot)\) None 0 1
147.1.d \(\chi_{147}(97, \cdot)\) None 0 1
147.1.f \(\chi_{147}(19, \cdot)\) None 0 2
147.1.h \(\chi_{147}(116, \cdot)\) None 0 2
147.1.j \(\chi_{147}(13, \cdot)\) None 0 6
147.1.l \(\chi_{147}(8, \cdot)\) 147.1.l.a 6 6
147.1.n \(\chi_{147}(2, \cdot)\) None 0 12
147.1.p \(\chi_{147}(10, \cdot)\) None 0 12