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Properties

Label 671.1
Level 671
Weight 1
Dimension 18
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 37200
Trace bound 1

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Defining parameters

Level: \( N \) = \( 671 = 11 \cdot 61 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(37200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(671))\).

Total New Old
Modular forms 618 548 70
Cusp forms 18 18 0
Eisenstein series 600 530 70

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 4 0 0

Trace form

\( 18 q - 2 q^{3} + 12 q^{4} + 8 q^{9} + O(q^{10}) \) \( 18 q - 2 q^{3} + 12 q^{4} + 8 q^{9} - 4 q^{11} - 6 q^{12} - 2 q^{14} - 4 q^{15} + 12 q^{16} - 6 q^{20} - 2 q^{22} + 12 q^{25} + 2 q^{26} - 4 q^{27} + 2 q^{31} - 8 q^{34} + 6 q^{36} - 8 q^{37} + 4 q^{38} - 8 q^{42} - 8 q^{45} - 4 q^{47} - 10 q^{48} + 12 q^{49} - 2 q^{55} - 6 q^{56} - 8 q^{58} + 2 q^{59} - 12 q^{60} + 4 q^{64} - 4 q^{66} + 2 q^{67} - 4 q^{70} + 2 q^{71} - 6 q^{75} - 2 q^{77} - 12 q^{80} + 14 q^{81} - 4 q^{82} - 2 q^{86} - 4 q^{88} + 2 q^{91} - 4 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(671))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
671.1.b \(\chi_{671}(428, \cdot)\) None 0 1
671.1.d \(\chi_{671}(670, \cdot)\) 671.1.d.a 1 1
671.1.d.b 1
671.1.d.c 2
671.1.d.d 2
671.1.d.e 4
671.1.d.f 4
671.1.g \(\chi_{671}(111, \cdot)\) None 0 2
671.1.n \(\chi_{671}(109, \cdot)\) None 0 2
671.1.p \(\chi_{671}(230, \cdot)\) 671.1.p.a 4 2
671.1.r \(\chi_{671}(95, \cdot)\) None 0 4
671.1.s \(\chi_{671}(186, \cdot)\) None 0 4
671.1.t \(\chi_{671}(393, \cdot)\) None 0 4
671.1.u \(\chi_{671}(182, \cdot)\) None 0 4
671.1.v \(\chi_{671}(41, \cdot)\) None 0 4
671.1.w \(\chi_{671}(149, \cdot)\) None 0 4
671.1.y \(\chi_{671}(62, \cdot)\) None 0 4
671.1.z \(\chi_{671}(131, \cdot)\) None 0 4
671.1.bb \(\chi_{671}(217, \cdot)\) None 0 4
671.1.be \(\chi_{671}(156, \cdot)\) None 0 4
671.1.bg \(\chi_{671}(447, \cdot)\) None 0 4
671.1.bh \(\chi_{671}(52, \cdot)\) None 0 4
671.1.bi \(\chi_{671}(265, \cdot)\) None 0 4
671.1.bq \(\chi_{671}(37, \cdot)\) None 0 8
671.1.bs \(\chi_{671}(114, \cdot)\) None 0 8
671.1.bu \(\chi_{671}(38, \cdot)\) None 0 8
671.1.bx \(\chi_{671}(69, \cdot)\) None 0 8
671.1.bz \(\chi_{671}(23, \cdot)\) None 0 8
671.1.ca \(\chi_{671}(355, \cdot)\) None 0 8
671.1.cc \(\chi_{671}(39, \cdot)\) None 0 8
671.1.cd \(\chi_{671}(134, \cdot)\) None 0 8
671.1.cg \(\chi_{671}(117, \cdot)\) None 0 8
671.1.ci \(\chi_{671}(76, \cdot)\) None 0 8
671.1.cj \(\chi_{671}(13, \cdot)\) None 0 8
671.1.cl \(\chi_{671}(57, \cdot)\) None 0 8
671.1.cn \(\chi_{671}(46, \cdot)\) None 0 8
671.1.co \(\chi_{671}(292, \cdot)\) None 0 8
671.1.cp \(\chi_{671}(107, \cdot)\) None 0 8
671.1.cq \(\chi_{671}(65, \cdot)\) None 0 8
671.1.cr \(\chi_{671}(19, \cdot)\) None 0 8
671.1.cs \(\chi_{671}(73, \cdot)\) None 0 8
671.1.cv \(\chi_{671}(71, \cdot)\) None 0 16
671.1.cx \(\chi_{671}(82, \cdot)\) None 0 16
671.1.cy \(\chi_{671}(67, \cdot)\) None 0 16
671.1.da \(\chi_{671}(115, \cdot)\) None 0 16
671.1.dd \(\chi_{671}(26, \cdot)\) None 0 16
671.1.df \(\chi_{671}(31, \cdot)\) None 0 16