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Properties

Label 3789.1
Level 3789
Weight 1
Dimension 70
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 1063440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3789 = 3^{2} \cdot 421 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(1063440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3789))\).

Total New Old
Modular forms 3584 1956 1628
Cusp forms 224 70 154
Eisenstein series 3360 1886 1474

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 70 0 0 0

Trace form

\( 70 q + O(q^{10}) \) \( 70 q + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3789))\)

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
3789.1.b \(\chi_{3789}(422, \cdot)\) None 0 1
3789.1.d \(\chi_{3789}(3788, \cdot)\) None 0 1
3789.1.i \(\chi_{3789}(1234, \cdot)\) 3789.1.i.a 2 2
3789.1.l \(\chi_{3789}(821, \cdot)\) None 0 2
3789.1.n \(\chi_{3789}(1262, \cdot)\) None 0 2
3789.1.o \(\chi_{3789}(2927, \cdot)\) None 0 2
3789.1.p \(\chi_{3789}(863, \cdot)\) None 0 2
3789.1.t \(\chi_{3789}(20, \cdot)\) None 0 2
3789.1.u \(\chi_{3789}(1685, \cdot)\) None 0 2
3789.1.v \(\chi_{3789}(2546, \cdot)\) None 0 2
3789.1.w \(\chi_{3789}(401, \cdot)\) None 0 2
3789.1.y \(\chi_{3789}(44, \cdot)\) None 0 4
3789.1.ba \(\chi_{3789}(377, \cdot)\) None 0 4
3789.1.bb \(\chi_{3789}(580, \cdot)\) None 0 4
3789.1.bg \(\chi_{3789}(262, \cdot)\) None 0 4
3789.1.bh \(\chi_{3789}(871, \cdot)\) None 0 4
3789.1.bi \(\chi_{3789}(1030, \cdot)\) None 0 4
3789.1.bj \(\chi_{3789}(269, \cdot)\) None 0 6
3789.1.bl \(\chi_{3789}(152, \cdot)\) None 0 6
3789.1.br \(\chi_{3789}(829, \cdot)\) 3789.1.br.a 8 8
3789.1.bx \(\chi_{3789}(415, \cdot)\) 3789.1.bx.a 12 12
3789.1.by \(\chi_{3789}(77, \cdot)\) None 0 8
3789.1.bz \(\chi_{3789}(35, \cdot)\) None 0 8
3789.1.ca \(\chi_{3789}(1094, \cdot)\) None 0 8
3789.1.cb \(\chi_{3789}(344, \cdot)\) None 0 8
3789.1.cf \(\chi_{3789}(314, \cdot)\) None 0 8
3789.1.cg \(\chi_{3789}(38, \cdot)\) None 0 8
3789.1.ch \(\chi_{3789}(488, \cdot)\) None 0 8
3789.1.cj \(\chi_{3789}(383, \cdot)\) None 0 8
3789.1.cl \(\chi_{3789}(245, \cdot)\) None 0 12
3789.1.cm \(\chi_{3789}(530, \cdot)\) None 0 12
3789.1.cn \(\chi_{3789}(668, \cdot)\) None 0 12
3789.1.co \(\chi_{3789}(149, \cdot)\) None 0 12
3789.1.cs \(\chi_{3789}(1034, \cdot)\) None 0 12
3789.1.ct \(\chi_{3789}(86, \cdot)\) None 0 12
3789.1.cu \(\chi_{3789}(767, \cdot)\) None 0 12
3789.1.cw \(\chi_{3789}(122, \cdot)\) None 0 12
3789.1.cx \(\chi_{3789}(148, \cdot)\) None 0 16
3789.1.cy \(\chi_{3789}(13, \cdot)\) None 0 16
3789.1.cz \(\chi_{3789}(73, \cdot)\) None 0 16
3789.1.de \(\chi_{3789}(34, \cdot)\) None 0 16
3789.1.df \(\chi_{3789}(296, \cdot)\) None 0 24
3789.1.dh \(\chi_{3789}(80, \cdot)\) None 0 24
3789.1.di \(\chi_{3789}(250, \cdot)\) None 0 24
3789.1.dj \(\chi_{3789}(70, \cdot)\) None 0 24
3789.1.dk \(\chi_{3789}(226, \cdot)\) None 0 24
3789.1.dp \(\chi_{3789}(52, \cdot)\) None 0 24
3789.1.du \(\chi_{3789}(10, \cdot)\) 3789.1.du.a 48 48
3789.1.dw \(\chi_{3789}(266, \cdot)\) None 0 48
3789.1.dy \(\chi_{3789}(104, \cdot)\) None 0 48
3789.1.dz \(\chi_{3789}(5, \cdot)\) None 0 48
3789.1.ea \(\chi_{3789}(17, \cdot)\) None 0 48
3789.1.ee \(\chi_{3789}(11, \cdot)\) None 0 48
3789.1.ef \(\chi_{3789}(68, \cdot)\) None 0 48
3789.1.eg \(\chi_{3789}(26, \cdot)\) None 0 48
3789.1.eh \(\chi_{3789}(101, \cdot)\) None 0 48
3789.1.ei \(\chi_{3789}(193, \cdot)\) None 0 96
3789.1.en \(\chi_{3789}(136, \cdot)\) None 0 96
3789.1.eo \(\chi_{3789}(61, \cdot)\) None 0 96
3789.1.ep \(\chi_{3789}(22, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3789))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3789)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(421))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1263))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3789))\)\(^{\oplus 1}\)