Properties

Label 168.1
Level 168
Weight 1
Dimension 4
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 1536
Trace bound 0

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Defining parameters

Level: \( N \) = \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(1536\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(168))\).

Total New Old
Modular forms 154 24 130
Cusp forms 10 4 6
Eisenstein series 144 20 124

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

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

Trace form

\( 4q - 2q^{4} + 4q^{6} - 2q^{7} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{4} + 4q^{6} - 2q^{7} - 2q^{9} + 2q^{10} - 4q^{15} - 2q^{16} - 4q^{22} - 2q^{24} - 2q^{28} + 2q^{31} + 2q^{33} + 4q^{36} + 2q^{40} - 2q^{42} - 2q^{49} - 2q^{54} + 4q^{55} + 2q^{58} + 2q^{60} + 4q^{63} + 4q^{64} + 2q^{70} - 4q^{73} + 2q^{79} - 2q^{81} + 2q^{87} + 2q^{88} - 4q^{90} - 2q^{96} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)

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
168.1.d \(\chi_{168}(113, \cdot)\) None 0 1
168.1.e \(\chi_{168}(83, \cdot)\) None 0 1
168.1.f \(\chi_{168}(97, \cdot)\) None 0 1
168.1.g \(\chi_{168}(43, \cdot)\) None 0 1
168.1.l \(\chi_{168}(13, \cdot)\) None 0 1
168.1.m \(\chi_{168}(127, \cdot)\) None 0 1
168.1.n \(\chi_{168}(29, \cdot)\) None 0 1
168.1.o \(\chi_{168}(167, \cdot)\) None 0 1
168.1.r \(\chi_{168}(47, \cdot)\) None 0 2
168.1.s \(\chi_{168}(53, \cdot)\) 168.1.s.a 2 2
168.1.s.b 2
168.1.w \(\chi_{168}(79, \cdot)\) None 0 2
168.1.x \(\chi_{168}(61, \cdot)\) None 0 2
168.1.y \(\chi_{168}(67, \cdot)\) None 0 2
168.1.z \(\chi_{168}(73, \cdot)\) None 0 2
168.1.be \(\chi_{168}(59, \cdot)\) None 0 2
168.1.bf \(\chi_{168}(65, \cdot)\) None 0 2

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(168))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(168)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)