Properties

Label 1067.1
Level 1067
Weight 1
Dimension 51
Nonzero newspaces 9
Newform subspaces 12
Sturm bound 94080
Trace bound 15

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Defining parameters

Level: \( N \) = \( 1067 = 11 \cdot 97 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 12 \)
Sturm bound: \(94080\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1067))\).

Total New Old
Modular forms 1011 905 106
Cusp forms 51 51 0
Eisenstein series 960 854 106

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 51 0 0 0

Trace form

\( 51 q - 2 q^{3} + 3 q^{4} - 2 q^{5} - 3 q^{9} + O(q^{10}) \) \( 51 q - 2 q^{3} + 3 q^{4} - 2 q^{5} - 3 q^{9} - q^{11} - 2 q^{12} - 4 q^{15} + 3 q^{16} - 2 q^{20} - 2 q^{23} + q^{25} - 4 q^{27} - 6 q^{31} - 6 q^{33} - 3 q^{36} - 2 q^{37} - q^{44} - 6 q^{45} - 6 q^{47} - 2 q^{48} + 3 q^{49} - 6 q^{53} - 2 q^{55} - 2 q^{59} - 4 q^{60} + 3 q^{64} - 2 q^{67} - 4 q^{69} - 2 q^{71} - 6 q^{75} - 2 q^{80} + 39 q^{81} - 2 q^{89} - 4 q^{91} - 2 q^{92} - 4 q^{93} - q^{97} - 3 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1067))\)

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
1067.1.b \(\chi_{1067}(1066, \cdot)\) 1067.1.b.a 1 1
1067.1.b.b 1
1067.1.b.c 1
1067.1.b.d 2
1067.1.c \(\chi_{1067}(98, \cdot)\) None 0 1
1067.1.g \(\chi_{1067}(560, \cdot)\) 1067.1.g.a 2 2
1067.1.j \(\chi_{1067}(714, \cdot)\) 1067.1.j.a 2 2
1067.1.k \(\chi_{1067}(230, \cdot)\) 1067.1.k.a 2 2
1067.1.l \(\chi_{1067}(241, \cdot)\) 1067.1.l.a 4 4
1067.1.o \(\chi_{1067}(195, \cdot)\) None 0 4
1067.1.p \(\chi_{1067}(96, \cdot)\) None 0 4
1067.1.q \(\chi_{1067}(285, \cdot)\) 1067.1.q.a 4 4
1067.1.u \(\chi_{1067}(109, \cdot)\) 1067.1.u.a 8 8
1067.1.v \(\chi_{1067}(172, \cdot)\) None 0 8
1067.1.y \(\chi_{1067}(43, \cdot)\) 1067.1.y.a 8 8
1067.1.z \(\chi_{1067}(62, \cdot)\) None 0 8
1067.1.ba \(\chi_{1067}(35, \cdot)\) None 0 8
1067.1.bd \(\chi_{1067}(34, \cdot)\) None 0 16
1067.1.bf \(\chi_{1067}(50, \cdot)\) None 0 16
1067.1.bg \(\chi_{1067}(32, \cdot)\) 1067.1.bg.a 16 16
1067.1.bj \(\chi_{1067}(6, \cdot)\) None 0 16
1067.1.bk \(\chi_{1067}(8, \cdot)\) None 0 32
1067.1.bm \(\chi_{1067}(23, \cdot)\) None 0 32
1067.1.bo \(\chi_{1067}(24, \cdot)\) None 0 32
1067.1.bq \(\chi_{1067}(20, \cdot)\) None 0 64
1067.1.bt \(\chi_{1067}(2, \cdot)\) None 0 64
1067.1.bv \(\chi_{1067}(5, \cdot)\) None 0 128