Properties

Label 931.1
Level 931
Weight 1
Dimension 30
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 70560
Trace bound 4

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Defining parameters

Level: \( N \) = \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(70560\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(931))\).

Total New Old
Modular forms 1122 855 267
Cusp forms 42 30 12
Eisenstein series 1080 825 255

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 22 8 0 0

Trace form

\( 30q + 2q^{2} + q^{4} - 4q^{5} - 8q^{8} + q^{9} + O(q^{10}) \) \( 30q + 2q^{2} + q^{4} - 4q^{5} - 8q^{8} + q^{9} - 4q^{11} - 4q^{15} - q^{16} + 2q^{17} + q^{19} + 2q^{20} - 2q^{23} - 3q^{25} - 3q^{28} + 4q^{29} - 4q^{30} - 3q^{35} + q^{36} + 4q^{39} - 8q^{43} - 4q^{44} + 17q^{45} - 4q^{46} - 4q^{47} - 2q^{51} - 2q^{53} + 13q^{55} - 4q^{57} + 4q^{58} - 4q^{61} + 9q^{64} - 4q^{65} + 2q^{67} + 2q^{68} + 4q^{71} - 4q^{73} - 5q^{76} + 4q^{78} + 2q^{79} - 4q^{80} - q^{81} + 2q^{83} - 12q^{85} + 2q^{86} - 4q^{92} - 6q^{95} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(931))\)

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
931.1.b \(\chi_{931}(246, \cdot)\) 931.1.b.a 1 1
931.1.b.b 1
931.1.d \(\chi_{931}(685, \cdot)\) None 0 1
931.1.j \(\chi_{931}(312, \cdot)\) None 0 2
931.1.k \(\chi_{931}(68, \cdot)\) 931.1.k.a 4 2
931.1.l \(\chi_{931}(362, \cdot)\) None 0 2
931.1.m \(\chi_{931}(391, \cdot)\) None 0 2
931.1.n \(\chi_{931}(753, \cdot)\) None 0 2
931.1.q \(\chi_{931}(50, \cdot)\) None 0 2
931.1.r \(\chi_{931}(18, \cdot)\) 931.1.r.a 2 2
931.1.t \(\chi_{931}(558, \cdot)\) 931.1.t.a 4 2
931.1.y \(\chi_{931}(20, \cdot)\) None 0 6
931.1.ba \(\chi_{931}(113, \cdot)\) 931.1.ba.a 6 6
931.1.bb \(\chi_{931}(215, \cdot)\) None 0 6
931.1.bc \(\chi_{931}(195, \cdot)\) None 0 6
931.1.bd \(\chi_{931}(80, \cdot)\) None 0 6
931.1.bg \(\chi_{931}(148, \cdot)\) None 0 6
931.1.bh \(\chi_{931}(116, \cdot)\) None 0 6
931.1.bi \(\chi_{931}(67, \cdot)\) None 0 6
931.1.bo \(\chi_{931}(26, \cdot)\) None 0 12
931.1.bq \(\chi_{931}(37, \cdot)\) 931.1.bq.a 12 12
931.1.br \(\chi_{931}(8, \cdot)\) None 0 12
931.1.bu \(\chi_{931}(65, \cdot)\) None 0 12
931.1.bv \(\chi_{931}(83, \cdot)\) None 0 12
931.1.bw \(\chi_{931}(96, \cdot)\) None 0 12
931.1.bx \(\chi_{931}(45, \cdot)\) None 0 12
931.1.by \(\chi_{931}(46, \cdot)\) None 0 12
931.1.ce \(\chi_{931}(2, \cdot)\) None 0 36
931.1.cf \(\chi_{931}(15, \cdot)\) None 0 36
931.1.cg \(\chi_{931}(51, \cdot)\) None 0 36
931.1.cj \(\chi_{931}(5, \cdot)\) None 0 36
931.1.ck \(\chi_{931}(17, \cdot)\) None 0 36
931.1.cl \(\chi_{931}(6, \cdot)\) None 0 36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(931))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(931)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 2}\)