Properties

Label 129.1
Level 129
Weight 1
Dimension 6
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1232
Trace bound 0

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Defining parameters

Level: \( N \) = \( 129 = 3 \cdot 43 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(1232\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(129))\).

Total New Old
Modular forms 90 46 44
Cusp forms 6 6 0
Eisenstein series 84 40 44

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(129))\)

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
129.1.b \(\chi_{129}(85, \cdot)\) None 0 1
129.1.c \(\chi_{129}(44, \cdot)\) None 0 1
129.1.f \(\chi_{129}(92, \cdot)\) None 0 2
129.1.g \(\chi_{129}(7, \cdot)\) None 0 2
129.1.k \(\chi_{129}(22, \cdot)\) None 0 6
129.1.l \(\chi_{129}(11, \cdot)\) 129.1.l.a 6 6
129.1.o \(\chi_{129}(14, \cdot)\) None 0 12
129.1.p \(\chi_{129}(19, \cdot)\) None 0 12