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Properties

Label 3400.1
Level 3400
Weight 1
Dimension 221
Nonzero newspaces 12
Newform subspaces 37
Sturm bound 691200
Trace bound 59

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Defining parameters

Level: \( N \) = \( 3400 = 2^{3} \cdot 5^{2} \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 37 \)
Sturm bound: \(691200\)
Trace bound: \(59\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3400))\).

Total New Old
Modular forms 6110 1451 4659
Cusp forms 734 221 513
Eisenstein series 5376 1230 4146

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 221 0 0 0

Trace form

\( 221 q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{8} + 7 q^{9} + O(q^{10}) \) \( 221 q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{8} + 7 q^{9} + 2 q^{11} - 6 q^{12} - 19 q^{16} + q^{17} + 3 q^{18} + 6 q^{19} + 2 q^{22} - 6 q^{24} - 4 q^{26} - 4 q^{27} - 8 q^{31} + q^{32} + 4 q^{33} - 11 q^{34} - 13 q^{36} - 14 q^{38} - 6 q^{41} + 26 q^{43} + 2 q^{44} + 8 q^{46} + 2 q^{48} + q^{49} - 14 q^{51} - 4 q^{54} - 8 q^{56} - 4 q^{57} + 22 q^{59} + q^{64} - 28 q^{66} + 2 q^{67} + q^{68} - 8 q^{71} + 3 q^{72} + 2 q^{73} - 2 q^{76} - 15 q^{81} + 2 q^{82} - 14 q^{83} - 22 q^{86} + 2 q^{88} + 6 q^{89} + 4 q^{94} + 2 q^{96} + 2 q^{97} - 7 q^{98} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3400))\)

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
3400.1.b \(\chi_{3400}(2551, \cdot)\) None 0 1
3400.1.d \(\chi_{3400}(3399, \cdot)\) None 0 1
3400.1.g \(\chi_{3400}(2651, \cdot)\) 3400.1.g.a 1 1
3400.1.g.b 2
3400.1.g.c 2
3400.1.g.d 2
3400.1.g.e 2
3400.1.g.f 2
3400.1.g.g 2
3400.1.i \(\chi_{3400}(3299, \cdot)\) None 0 1
3400.1.k \(\chi_{3400}(1699, \cdot)\) 3400.1.k.a 2 1
3400.1.k.b 4
3400.1.m \(\chi_{3400}(851, \cdot)\) None 0 1
3400.1.n \(\chi_{3400}(1599, \cdot)\) None 0 1
3400.1.p \(\chi_{3400}(951, \cdot)\) None 0 1
3400.1.r \(\chi_{3400}(1857, \cdot)\) None 0 2
3400.1.s \(\chi_{3400}(293, \cdot)\) 3400.1.s.a 4 2
3400.1.v \(\chi_{3400}(1257, \cdot)\) None 0 2
3400.1.w \(\chi_{3400}(1157, \cdot)\) None 0 2
3400.1.y \(\chi_{3400}(251, \cdot)\) 3400.1.y.a 2 2
3400.1.y.b 4
3400.1.y.c 4
3400.1.bb \(\chi_{3400}(599, \cdot)\) None 0 2
3400.1.bc \(\chi_{3400}(2299, \cdot)\) 3400.1.bc.a 2 2
3400.1.bc.b 2
3400.1.bc.c 4
3400.1.bc.d 4
3400.1.bf \(\chi_{3400}(1551, \cdot)\) None 0 2
3400.1.bh \(\chi_{3400}(2857, \cdot)\) None 0 2
3400.1.bi \(\chi_{3400}(2957, \cdot)\) None 0 2
3400.1.bk \(\chi_{3400}(157, \cdot)\) 3400.1.bk.a 4 2
3400.1.bn \(\chi_{3400}(1993, \cdot)\) None 0 2
3400.1.bq \(\chi_{3400}(151, \cdot)\) None 0 4
3400.1.br \(\chi_{3400}(699, \cdot)\) 3400.1.br.a 4 4
3400.1.br.b 4
3400.1.br.c 8
3400.1.br.d 8
3400.1.bu \(\chi_{3400}(257, \cdot)\) None 0 4
3400.1.bv \(\chi_{3400}(393, \cdot)\) None 0 4
3400.1.by \(\chi_{3400}(757, \cdot)\) None 0 4
3400.1.bz \(\chi_{3400}(93, \cdot)\) None 0 4
3400.1.cb \(\chi_{3400}(399, \cdot)\) None 0 4
3400.1.ce \(\chi_{3400}(451, \cdot)\) 3400.1.ce.a 4 4
3400.1.ce.b 8
3400.1.ce.c 8
3400.1.cf \(\chi_{3400}(171, \cdot)\) None 0 4
3400.1.ch \(\chi_{3400}(339, \cdot)\) 3400.1.ch.a 16 4
3400.1.cj \(\chi_{3400}(271, \cdot)\) None 0 4
3400.1.cl \(\chi_{3400}(239, \cdot)\) None 0 4
3400.1.cn \(\chi_{3400}(679, \cdot)\) None 0 4
3400.1.cp \(\chi_{3400}(511, \cdot)\) None 0 4
3400.1.cq \(\chi_{3400}(579, \cdot)\) None 0 4
3400.1.cs \(\chi_{3400}(611, \cdot)\) 3400.1.cs.a 4 4
3400.1.cs.b 4
3400.1.cs.c 8
3400.1.cu \(\chi_{3400}(7, \cdot)\) None 0 8
3400.1.cx \(\chi_{3400}(107, \cdot)\) 3400.1.cx.a 8 8
3400.1.cx.b 8
3400.1.cx.c 16
3400.1.cx.d 16
3400.1.cz \(\chi_{3400}(201, \cdot)\) None 0 8
3400.1.da \(\chi_{3400}(301, \cdot)\) None 0 8
3400.1.dc \(\chi_{3400}(549, \cdot)\) None 0 8
3400.1.df \(\chi_{3400}(249, \cdot)\) None 0 8
3400.1.dh \(\chi_{3400}(243, \cdot)\) 3400.1.dh.a 8 8
3400.1.dh.b 8
3400.1.dh.c 16
3400.1.dh.d 16
3400.1.di \(\chi_{3400}(143, \cdot)\) None 0 8
3400.1.dl \(\chi_{3400}(13, \cdot)\) None 0 8
3400.1.dm \(\chi_{3400}(217, \cdot)\) None 0 8
3400.1.dp \(\chi_{3400}(237, \cdot)\) None 0 8
3400.1.dq \(\chi_{3400}(137, \cdot)\) None 0 8
3400.1.ds \(\chi_{3400}(191, \cdot)\) None 0 8
3400.1.dv \(\chi_{3400}(259, \cdot)\) None 0 8
3400.1.dw \(\chi_{3400}(319, \cdot)\) None 0 8
3400.1.dz \(\chi_{3400}(531, \cdot)\) None 0 8
3400.1.eb \(\chi_{3400}(477, \cdot)\) None 0 8
3400.1.ec \(\chi_{3400}(33, \cdot)\) None 0 8
3400.1.ee \(\chi_{3400}(353, \cdot)\) None 0 8
3400.1.eh \(\chi_{3400}(973, \cdot)\) None 0 8
3400.1.ei \(\chi_{3400}(291, \cdot)\) None 0 16
3400.1.el \(\chi_{3400}(359, \cdot)\) None 0 16
3400.1.em \(\chi_{3400}(53, \cdot)\) None 0 16
3400.1.ep \(\chi_{3400}(117, \cdot)\) None 0 16
3400.1.eq \(\chi_{3400}(433, \cdot)\) None 0 16
3400.1.et \(\chi_{3400}(297, \cdot)\) None 0 16
3400.1.ev \(\chi_{3400}(19, \cdot)\) None 0 16
3400.1.ew \(\chi_{3400}(111, \cdot)\) None 0 16
3400.1.ez \(\chi_{3400}(23, \cdot)\) None 0 32
3400.1.fa \(\chi_{3400}(3, \cdot)\) None 0 32
3400.1.fc \(\chi_{3400}(129, \cdot)\) None 0 32
3400.1.ff \(\chi_{3400}(29, \cdot)\) None 0 32
3400.1.fh \(\chi_{3400}(61, \cdot)\) None 0 32
3400.1.fi \(\chi_{3400}(41, \cdot)\) None 0 32
3400.1.fk \(\chi_{3400}(163, \cdot)\) None 0 32
3400.1.fn \(\chi_{3400}(63, \cdot)\) None 0 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3400))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3400)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1700))\)\(^{\oplus 2}\)