Properties

Label 133.1
Level 133
Weight 1
Dimension 6
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 1440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 133 = 7 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(1440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(133))\).

Total New Old
Modular forms 114 90 24
Cusp forms 6 6 0
Eisenstein series 108 84 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 4 0 0

Trace form

\( 6q - 2q^{2} - q^{4} + q^{5} - q^{7} - 4q^{8} - q^{9} + O(q^{10}) \) \( 6q - 2q^{2} - q^{4} + q^{5} - q^{7} - 4q^{8} - q^{9} + q^{11} - 2q^{15} + q^{16} - 2q^{17} - q^{19} - 2q^{20} + 2q^{21} - q^{23} + 2q^{28} + 2q^{29} + 4q^{30} - q^{35} + 2q^{36} - 4q^{39} + 2q^{42} - 4q^{43} + q^{44} + q^{45} + 4q^{46} + q^{47} - 5q^{49} + 2q^{51} + 2q^{53} + 2q^{55} - 2q^{57} - 4q^{58} + q^{61} - q^{63} + 6q^{64} + 4q^{65} - 2q^{67} - 2q^{68} - 2q^{70} + 2q^{71} + q^{73} + 2q^{76} - 2q^{77} + 2q^{78} - 2q^{79} + q^{80} + q^{81} - 2q^{83} - 6q^{85} - 2q^{86} + 2q^{91} - 2q^{92} + 3q^{95} + 2q^{98} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(133))\)

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
133.1.b \(\chi_{133}(113, \cdot)\) None 0 1
133.1.d \(\chi_{133}(20, \cdot)\) None 0 1
133.1.j \(\chi_{133}(46, \cdot)\) None 0 2
133.1.k \(\chi_{133}(45, \cdot)\) None 0 2
133.1.l \(\chi_{133}(96, \cdot)\) None 0 2
133.1.m \(\chi_{133}(83, \cdot)\) 133.1.m.a 4 2
133.1.n \(\chi_{133}(65, \cdot)\) None 0 2
133.1.q \(\chi_{133}(8, \cdot)\) None 0 2
133.1.r \(\chi_{133}(18, \cdot)\) 133.1.r.a 2 2
133.1.t \(\chi_{133}(26, \cdot)\) None 0 2
133.1.x \(\chi_{133}(17, \cdot)\) None 0 6
133.1.y \(\chi_{133}(6, \cdot)\) None 0 6
133.1.z \(\chi_{133}(5, \cdot)\) None 0 6
133.1.bc \(\chi_{133}(15, \cdot)\) None 0 6
133.1.bd \(\chi_{133}(51, \cdot)\) None 0 6
133.1.be \(\chi_{133}(2, \cdot)\) None 0 6