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Properties

Label 3159.1
Level 3159
Weight 1
Dimension 114
Nonzero newspaces 13
Newform subspaces 45
Sturm bound 734832
Trace bound 28

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Defining parameters

Level: \( N \) = \( 3159 = 3^{5} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 13 \)
Newform subspaces: \( 45 \)
Sturm bound: \(734832\)
Trace bound: \(28\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3159))\).

Total New Old
Modular forms 4765 2226 2539
Cusp forms 229 114 115
Eisenstein series 4536 2112 2424

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 102 0 12 0

Trace form

\( 114 q + O(q^{10}) \) \( 114 q - 12 q^{10} + 6 q^{19} - 12 q^{55} + 42 q^{64} - 24 q^{73} + 3 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3159))\)

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
3159.1.c \(\chi_{3159}(1457, \cdot)\) None 0 1
3159.1.d \(\chi_{3159}(3158, \cdot)\) 3159.1.d.a 1 1
3159.1.d.b 1
3159.1.d.c 1
3159.1.d.d 1
3159.1.d.e 1
3159.1.d.f 1
3159.1.d.g 2
3159.1.d.h 2
3159.1.d.i 2
3159.1.d.j 2
3159.1.j \(\chi_{3159}(1945, \cdot)\) 3159.1.j.a 4 2
3159.1.k \(\chi_{3159}(809, \cdot)\) 3159.1.k.a 2 2
3159.1.k.b 2
3159.1.k.c 4
3159.1.m \(\chi_{3159}(647, \cdot)\) 3159.1.m.a 2 2
3159.1.m.b 2
3159.1.n \(\chi_{3159}(1052, \cdot)\) 3159.1.n.a 2 2
3159.1.n.b 2
3159.1.n.c 2
3159.1.n.d 2
3159.1.n.e 2
3159.1.n.f 2
3159.1.n.g 2
3159.1.n.h 2
3159.1.n.i 4
3159.1.n.j 4
3159.1.n.k 4
3159.1.o \(\chi_{3159}(485, \cdot)\) 3159.1.o.a 2 2
3159.1.o.b 2
3159.1.p \(\chi_{3159}(971, \cdot)\) 3159.1.p.a 2 2
3159.1.p.b 2
3159.1.p.c 4
3159.1.s \(\chi_{3159}(404, \cdot)\) None 0 2
3159.1.u \(\chi_{3159}(1862, \cdot)\) 3159.1.u.a 2 2
3159.1.u.b 2
3159.1.u.c 4
3159.1.v \(\chi_{3159}(2591, \cdot)\) 3159.1.v.a 2 2
3159.1.v.b 2
3159.1.z \(\chi_{3159}(1540, \cdot)\) 3159.1.z.a 4 4
3159.1.z.b 4
3159.1.bb \(\chi_{3159}(811, \cdot)\) 3159.1.bb.a 4 4
3159.1.bb.b 4
3159.1.be \(\chi_{3159}(163, \cdot)\) 3159.1.be.a 4 4
3159.1.be.b 4
3159.1.bg \(\chi_{3159}(487, \cdot)\) 3159.1.bg.a 4 4
3159.1.bg.b 4
3159.1.bh \(\chi_{3159}(134, \cdot)\) None 0 6
3159.1.bi \(\chi_{3159}(350, \cdot)\) None 0 6
3159.1.bj \(\chi_{3159}(296, \cdot)\) None 0 6
3159.1.bk \(\chi_{3159}(107, \cdot)\) None 0 6
3159.1.bm \(\chi_{3159}(53, \cdot)\) None 0 6
3159.1.bp \(\chi_{3159}(269, \cdot)\) None 0 6
3159.1.bu \(\chi_{3159}(28, \cdot)\) None 0 12
3159.1.bv \(\chi_{3159}(379, \cdot)\) None 0 12
3159.1.bx \(\chi_{3159}(109, \cdot)\) None 0 12
3159.1.ca \(\chi_{3159}(179, \cdot)\) None 0 18
3159.1.cb \(\chi_{3159}(170, \cdot)\) None 0 18
3159.1.cc \(\chi_{3159}(152, \cdot)\) None 0 18
3159.1.cf \(\chi_{3159}(116, \cdot)\) None 0 18
3159.1.cg \(\chi_{3159}(17, \cdot)\) None 0 18
3159.1.ch \(\chi_{3159}(35, \cdot)\) None 0 18
3159.1.cl \(\chi_{3159}(73, \cdot)\) None 0 36
3159.1.cm \(\chi_{3159}(19, \cdot)\) None 0 36
3159.1.cn \(\chi_{3159}(154, \cdot)\) None 0 36
3159.1.cr \(\chi_{3159}(29, \cdot)\) None 0 54
3159.1.ct \(\chi_{3159}(23, \cdot)\) None 0 54
3159.1.cu \(\chi_{3159}(38, \cdot)\) None 0 54
3159.1.cw \(\chi_{3159}(14, \cdot)\) None 0 54
3159.1.cy \(\chi_{3159}(68, \cdot)\) None 0 54
3159.1.cz \(\chi_{3159}(95, \cdot)\) None 0 54
3159.1.da \(\chi_{3159}(58, \cdot)\) None 0 108
3159.1.dc \(\chi_{3159}(31, \cdot)\) None 0 108
3159.1.de \(\chi_{3159}(7, \cdot)\) None 0 108

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3159))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3159)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1053))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3159))\)\(^{\oplus 1}\)