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Properties

Label 3891.1
Level 3891
Weight 1
Dimension 239
Nonzero newspaces 15
Newform subspaces 22
Sturm bound 1121472
Trace bound 19

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Defining parameters

Level: \( N \) = \( 3891 = 3 \cdot 1297 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 22 \)
Sturm bound: \(1121472\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3891))\).

Total New Old
Modular forms 2831 1533 1298
Cusp forms 239 239 0
Eisenstein series 2592 1294 1298

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 235 0 4 0

Trace form

\( 239 q - 2 q^{3} - q^{4} - 6 q^{7} + 6 q^{9} + O(q^{10}) \) \( 239 q - 2 q^{3} - q^{4} - 6 q^{7} + 6 q^{9} - 4 q^{10} - 6 q^{12} - 4 q^{13} + 21 q^{16} + 11 q^{18} - 2 q^{19} - 10 q^{21} - 5 q^{25} - 8 q^{27} - 10 q^{28} - 8 q^{30} - 4 q^{31} + 8 q^{34} + 4 q^{36} - 4 q^{37} - 2 q^{39} - 4 q^{43} + 11 q^{49} - 24 q^{52} - 4 q^{55} + 2 q^{57} + 8 q^{58} + 4 q^{61} - 12 q^{63} + q^{64} - 8 q^{70} - 11 q^{72} - 10 q^{73} - 4 q^{75} + 2 q^{76} - 2 q^{79} + 6 q^{81} - q^{84} - 4 q^{90} - 2 q^{91} - 6 q^{93} - 11 q^{96} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3891))\)

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
3891.1.b \(\chi_{3891}(1298, \cdot)\) None 0 1
3891.1.c \(\chi_{3891}(3890, \cdot)\) 3891.1.c.a 1 1
3891.1.c.b 1
3891.1.c.c 1
3891.1.c.d 2
3891.1.c.e 2
3891.1.c.f 4
3891.1.c.g 10
3891.1.g \(\chi_{3891}(2558, \cdot)\) 3891.1.g.a 2 2
3891.1.i \(\chi_{3891}(365, \cdot)\) 3891.1.i.a 2 2
3891.1.i.b 4
3891.1.j \(\chi_{3891}(932, \cdot)\) 3891.1.j.a 2 2
3891.1.l \(\chi_{3891}(2378, \cdot)\) 3891.1.l.a 4 4
3891.1.n \(\chi_{3891}(170, \cdot)\) 3891.1.n.a 4 4
3891.1.p \(\chi_{3891}(157, \cdot)\) None 0 8
3891.1.s \(\chi_{3891}(104, \cdot)\) 3891.1.s.a 6 6
3891.1.t \(\chi_{3891}(212, \cdot)\) 3891.1.t.a 6 6
3891.1.v \(\chi_{3891}(398, \cdot)\) 3891.1.v.a 8 8
3891.1.x \(\chi_{3891}(1775, \cdot)\) 3891.1.x.a 12 12
3891.1.ba \(\chi_{3891}(394, \cdot)\) None 0 16
3891.1.bb \(\chi_{3891}(290, \cdot)\) 3891.1.bb.a 18 18
3891.1.bc \(\chi_{3891}(200, \cdot)\) 3891.1.bc.a 18 18
3891.1.be \(\chi_{3891}(38, \cdot)\) 3891.1.be.a 24 24
3891.1.bh \(\chi_{3891}(14, \cdot)\) 3891.1.bh.a 36 36
3891.1.bk \(\chi_{3891}(34, \cdot)\) None 0 48
3891.1.bl \(\chi_{3891}(23, \cdot)\) None 0 54
3891.1.bn \(\chi_{3891}(56, \cdot)\) None 0 54
3891.1.bp \(\chi_{3891}(8, \cdot)\) 3891.1.bp.a 72 72
3891.1.br \(\chi_{3891}(26, \cdot)\) None 0 108
3891.1.bs \(\chi_{3891}(40, \cdot)\) None 0 144
3891.1.bu \(\chi_{3891}(2, \cdot)\) None 0 216
3891.1.bw \(\chi_{3891}(10, \cdot)\) None 0 432