Properties

Label 140.1
Level 140
Weight 1
Dimension 6
Nonzero newspaces 2
Newforms 4
Sturm bound 1152
Trace bound 1

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Defining parameters

Level: \( N \) = \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 4 \)
Sturm bound: \(1152\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(140))\).

Total New Old
Modular forms 126 38 88
Cusp forms 6 6 0
Eisenstein series 120 32 88

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

\( 6q - 2q^{4} - 2q^{5} - 4q^{6} + O(q^{10}) \) \( 6q - 2q^{4} - 2q^{5} - 4q^{6} - 2q^{11} + 4q^{14} - 2q^{15} - 2q^{16} + 4q^{20} + 2q^{24} - 6q^{29} + 2q^{30} + 2q^{35} + 2q^{39} - 4q^{41} + 2q^{46} + 2q^{51} - 2q^{54} - 2q^{56} + 2q^{61} + 4q^{64} - 2q^{65} + 4q^{69} - 2q^{70} + 4q^{71} - 2q^{79} - 2q^{80} - 4q^{84} - 2q^{85} + 2q^{86} + 2q^{89} - 2q^{91} - 4q^{94} + 2q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)

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
140.1.b \(\chi_{140}(71, \cdot)\) None 0 1
140.1.d \(\chi_{140}(41, \cdot)\) None 0 1
140.1.f \(\chi_{140}(99, \cdot)\) None 0 1
140.1.h \(\chi_{140}(69, \cdot)\) 140.1.h.a 1 1
140.1.h.b 1
140.1.j \(\chi_{140}(27, \cdot)\) None 0 2
140.1.l \(\chi_{140}(57, \cdot)\) None 0 2
140.1.n \(\chi_{140}(89, \cdot)\) None 0 2
140.1.p \(\chi_{140}(39, \cdot)\) 140.1.p.a 2 2
140.1.p.b 2
140.1.r \(\chi_{140}(61, \cdot)\) None 0 2
140.1.t \(\chi_{140}(11, \cdot)\) None 0 2
140.1.v \(\chi_{140}(37, \cdot)\) None 0 4
140.1.x \(\chi_{140}(3, \cdot)\) None 0 4