Properties

Label 968.1
Level 968
Weight 1
Dimension 76
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 58080
Trace bound 1

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Defining parameters

Level: \( N \) = \( 968 = 2^{3} \cdot 11^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 9 \)
Sturm bound: \(58080\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(968))\).

Total New Old
Modular forms 1076 357 719
Cusp forms 116 76 40
Eisenstein series 960 281 679

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 66 0 10 0

Trace form

\( 76 q + q^{2} + 2 q^{3} + q^{4} - 8 q^{6} + q^{8} + 3 q^{9} + O(q^{10}) \) \( 76 q + q^{2} + 2 q^{3} + q^{4} - 8 q^{6} + q^{8} + 3 q^{9} - 8 q^{12} + q^{16} + 2 q^{17} - 7 q^{18} - 8 q^{19} - 10 q^{23} - 8 q^{24} + q^{25} - 6 q^{27} - 9 q^{32} - 5 q^{33} - 8 q^{34} - 7 q^{36} + 2 q^{38} + 2 q^{41} + 2 q^{43} - 5 q^{44} + 2 q^{48} + q^{49} + q^{50} - 6 q^{51} + 4 q^{54} - 6 q^{57} - 8 q^{59} + q^{64} + 2 q^{67} + 2 q^{68} + 3 q^{72} + 2 q^{73} - 8 q^{75} + 2 q^{76} - 5 q^{81} - 8 q^{82} - 8 q^{83} - 8 q^{86} - 18 q^{89} + 2 q^{96} - 8 q^{97} - 9 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(968))\)

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
968.1.b \(\chi_{968}(725, \cdot)\) None 0 1
968.1.d \(\chi_{968}(727, \cdot)\) None 0 1
968.1.f \(\chi_{968}(243, \cdot)\) 968.1.f.a 2 1
968.1.f.b 2
968.1.h \(\chi_{968}(241, \cdot)\) 968.1.h.a 2 1
968.1.j \(\chi_{968}(161, \cdot)\) 968.1.j.a 8 4
968.1.l \(\chi_{968}(3, \cdot)\) 968.1.l.a 4 4
968.1.l.b 4
968.1.l.c 4
968.1.n \(\chi_{968}(487, \cdot)\) None 0 4
968.1.p \(\chi_{968}(645, \cdot)\) None 0 4
968.1.s \(\chi_{968}(23, \cdot)\) None 0 10
968.1.u \(\chi_{968}(21, \cdot)\) None 0 10
968.1.v \(\chi_{968}(65, \cdot)\) None 0 10
968.1.x \(\chi_{968}(67, \cdot)\) 968.1.x.a 10 10
968.1.z \(\chi_{968}(59, \cdot)\) 968.1.z.a 40 40
968.1.bb \(\chi_{968}(17, \cdot)\) None 0 40
968.1.bc \(\chi_{968}(13, \cdot)\) None 0 40
968.1.be \(\chi_{968}(15, \cdot)\) None 0 40

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(968))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(968)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 2}\)