Properties

Label 88.1
Level 88
Weight 1
Dimension 4
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 480
Trace bound 0

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Defining parameters

Level: \( N \) = \( 88 = 2^{3} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(480\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(88))\).

Total New Old
Modular forms 66 22 44
Cusp forms 6 4 2
Eisenstein series 60 18 42

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

\( 4q - q^{2} - 2q^{3} - q^{4} + 3q^{6} - q^{8} - 3q^{9} + O(q^{10}) \) \( 4q - q^{2} - 2q^{3} - q^{4} + 3q^{6} - q^{8} - 3q^{9} - q^{11} - 2q^{12} - q^{16} - 2q^{17} + 2q^{18} + 3q^{19} - q^{22} + 3q^{24} - q^{25} + q^{27} + 4q^{32} + 3q^{33} - 2q^{34} + 2q^{36} - 2q^{38} - 2q^{41} - 2q^{43} + 4q^{44} - 2q^{48} - q^{49} - q^{50} + q^{51} - 4q^{54} + q^{57} + 3q^{59} - q^{64} - 2q^{66} - 2q^{67} - 2q^{68} - 3q^{72} - 2q^{73} + 3q^{75} - 2q^{76} + 3q^{82} + 3q^{83} + 3q^{86} - q^{88} - 2q^{89} - 2q^{96} + 3q^{97} + 4q^{98} - 3q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)

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
88.1.b \(\chi_{88}(21, \cdot)\) None 0 1
88.1.d \(\chi_{88}(23, \cdot)\) None 0 1
88.1.f \(\chi_{88}(67, \cdot)\) None 0 1
88.1.h \(\chi_{88}(65, \cdot)\) None 0 1
88.1.j \(\chi_{88}(17, \cdot)\) None 0 4
88.1.l \(\chi_{88}(3, \cdot)\) 88.1.l.a 4 4
88.1.n \(\chi_{88}(15, \cdot)\) None 0 4
88.1.p \(\chi_{88}(13, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(88))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(88)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)