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Properties

Label 3528.1
Level 3528
Weight 1
Dimension 243
Nonzero newspaces 22
Newform subspaces 45
Sturm bound 677376
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 22 \)
Newform subspaces: \( 45 \)
Sturm bound: \(677376\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3528))\).

Total New Old
Modular forms 6658 1116 5542
Cusp forms 898 243 655
Eisenstein series 5760 873 4887

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 219 16 8 0

Trace form

\( 243 q + 3 q^{3} + 6 q^{4} + q^{6} + 3 q^{8} - q^{9} + O(q^{10}) \) \( 243 q + 3 q^{3} + 6 q^{4} + q^{6} + 3 q^{8} - q^{9} + 8 q^{10} + q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{15} + 6 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 13 q^{22} - 2 q^{23} + q^{24} + 12 q^{25} - 4 q^{26} + 6 q^{27} + 2 q^{30} - 14 q^{31} + 3 q^{33} - q^{34} - 15 q^{36} + 2 q^{37} - q^{38} + 4 q^{39} - 32 q^{40} - 5 q^{41} + 5 q^{43} + 6 q^{44} + 2 q^{46} + 9 q^{48} + 46 q^{50} - 3 q^{51} + q^{54} + 8 q^{55} + 11 q^{57} - 14 q^{58} - q^{59} + 4 q^{60} - 27 q^{64} - 2 q^{65} + 2 q^{66} + 5 q^{67} - 3 q^{68} - 6 q^{70} + 4 q^{71} - 7 q^{72} + 8 q^{73} + 2 q^{74} + q^{75} - 5 q^{76} + 32 q^{78} + 16 q^{79} - 9 q^{81} + 2 q^{82} - 2 q^{83} - q^{86} - 17 q^{88} - 4 q^{90} - 32 q^{92} + 8 q^{95} - 2 q^{96} + 3 q^{97} + 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3528))\)

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
3528.1.d \(\chi_{3528}(1961, \cdot)\) 3528.1.d.a 2 1
3528.1.d.b 2
3528.1.e \(\chi_{3528}(1763, \cdot)\) None 0 1
3528.1.f \(\chi_{3528}(2449, \cdot)\) None 0 1
3528.1.g \(\chi_{3528}(883, \cdot)\) 3528.1.g.a 1 1
3528.1.g.b 2
3528.1.g.c 2
3528.1.l \(\chi_{3528}(685, \cdot)\) 3528.1.l.a 4 1
3528.1.m \(\chi_{3528}(2647, \cdot)\) None 0 1
3528.1.n \(\chi_{3528}(197, \cdot)\) 3528.1.n.a 4 1
3528.1.o \(\chi_{3528}(3527, \cdot)\) None 0 1
3528.1.u \(\chi_{3528}(803, \cdot)\) 3528.1.u.a 16 2
3528.1.v \(\chi_{3528}(569, \cdot)\) None 0 2
3528.1.ba \(\chi_{3528}(67, \cdot)\) 3528.1.ba.a 2 2
3528.1.ba.b 2
3528.1.ba.c 4
3528.1.ba.d 4
3528.1.ba.e 8
3528.1.bb \(\chi_{3528}(313, \cdot)\) None 0 2
3528.1.bc \(\chi_{3528}(215, \cdot)\) None 0 2
3528.1.bd \(\chi_{3528}(557, \cdot)\) 3528.1.bd.a 8 2
3528.1.bg \(\chi_{3528}(1373, \cdot)\) 3528.1.bg.a 8 2
3528.1.bh \(\chi_{3528}(1391, \cdot)\) None 0 2
3528.1.bi \(\chi_{3528}(1157, \cdot)\) 3528.1.bi.a 8 2
3528.1.bj \(\chi_{3528}(1175, \cdot)\) None 0 2
3528.1.bn \(\chi_{3528}(1861, \cdot)\) None 0 2
3528.1.bo \(\chi_{3528}(655, \cdot)\) None 0 2
3528.1.bp \(\chi_{3528}(1501, \cdot)\) 3528.1.bp.a 2 2
3528.1.bp.b 2
3528.1.bp.c 4
3528.1.bq \(\chi_{3528}(295, \cdot)\) None 0 2
3528.1.bv \(\chi_{3528}(2431, \cdot)\) None 0 2
3528.1.bw \(\chi_{3528}(325, \cdot)\) 3528.1.bw.a 2 2
3528.1.bw.b 4
3528.1.bw.c 4
3528.1.bx \(\chi_{3528}(667, \cdot)\) 3528.1.bx.a 2 2
3528.1.bx.b 4
3528.1.bx.c 4
3528.1.by \(\chi_{3528}(2089, \cdot)\) None 0 2
3528.1.cd \(\chi_{3528}(97, \cdot)\) None 0 2
3528.1.ce \(\chi_{3528}(2419, \cdot)\) 3528.1.ce.a 2 2
3528.1.ce.b 2
3528.1.ce.c 4
3528.1.ce.d 4
3528.1.ce.e 8
3528.1.cf \(\chi_{3528}(1489, \cdot)\) None 0 2
3528.1.cg \(\chi_{3528}(2059, \cdot)\) 3528.1.cg.a 2 2
3528.1.cg.b 4
3528.1.cg.c 4
3528.1.cg.d 4
3528.1.cg.e 8
3528.1.cl \(\chi_{3528}(785, \cdot)\) None 0 2
3528.1.cm \(\chi_{3528}(227, \cdot)\) 3528.1.cm.a 16 2
3528.1.cn \(\chi_{3528}(1145, \cdot)\) None 0 2
3528.1.co \(\chi_{3528}(587, \cdot)\) 3528.1.co.a 16 2
3528.1.ct \(\chi_{3528}(1403, \cdot)\) 3528.1.ct.a 8 2
3528.1.cu \(\chi_{3528}(1745, \cdot)\) 3528.1.cu.a 4 2
3528.1.cv \(\chi_{3528}(79, \cdot)\) None 0 2
3528.1.cw \(\chi_{3528}(2077, \cdot)\) 3528.1.cw.a 2 2
3528.1.cw.b 2
3528.1.cw.c 4
3528.1.da \(\chi_{3528}(815, \cdot)\) None 0 2
3528.1.db \(\chi_{3528}(1733, \cdot)\) 3528.1.db.a 8 2
3528.1.de \(\chi_{3528}(503, \cdot)\) None 0 6
3528.1.df \(\chi_{3528}(701, \cdot)\) None 0 6
3528.1.dg \(\chi_{3528}(127, \cdot)\) None 0 6
3528.1.dh \(\chi_{3528}(181, \cdot)\) 3528.1.dh.a 12 6
3528.1.dm \(\chi_{3528}(379, \cdot)\) None 0 6
3528.1.dn \(\chi_{3528}(433, \cdot)\) None 0 6
3528.1.do \(\chi_{3528}(251, \cdot)\) None 0 6
3528.1.dp \(\chi_{3528}(449, \cdot)\) None 0 6
3528.1.dw \(\chi_{3528}(221, \cdot)\) None 0 12
3528.1.dx \(\chi_{3528}(47, \cdot)\) None 0 12
3528.1.eb \(\chi_{3528}(61, \cdot)\) None 0 12
3528.1.ec \(\chi_{3528}(319, \cdot)\) None 0 12
3528.1.ed \(\chi_{3528}(233, \cdot)\) None 0 12
3528.1.ee \(\chi_{3528}(395, \cdot)\) None 0 12
3528.1.ej \(\chi_{3528}(83, \cdot)\) None 0 12
3528.1.ek \(\chi_{3528}(137, \cdot)\) None 0 12
3528.1.el \(\chi_{3528}(131, \cdot)\) None 0 12
3528.1.em \(\chi_{3528}(113, \cdot)\) None 0 12
3528.1.er \(\chi_{3528}(43, \cdot)\) None 0 12
3528.1.es \(\chi_{3528}(241, \cdot)\) None 0 12
3528.1.et \(\chi_{3528}(403, \cdot)\) None 0 12
3528.1.eu \(\chi_{3528}(265, \cdot)\) None 0 12
3528.1.ez \(\chi_{3528}(73, \cdot)\) None 0 12
3528.1.fa \(\chi_{3528}(163, \cdot)\) None 0 12
3528.1.fb \(\chi_{3528}(397, \cdot)\) 3528.1.fb.a 24 12
3528.1.fc \(\chi_{3528}(415, \cdot)\) None 0 12
3528.1.fh \(\chi_{3528}(463, \cdot)\) None 0 12
3528.1.fi \(\chi_{3528}(229, \cdot)\) None 0 12
3528.1.fj \(\chi_{3528}(151, \cdot)\) None 0 12
3528.1.fk \(\chi_{3528}(13, \cdot)\) None 0 12
3528.1.fo \(\chi_{3528}(167, \cdot)\) None 0 12
3528.1.fp \(\chi_{3528}(149, \cdot)\) None 0 12
3528.1.fq \(\chi_{3528}(383, \cdot)\) None 0 12
3528.1.fr \(\chi_{3528}(29, \cdot)\) None 0 12
3528.1.fu \(\chi_{3528}(53, \cdot)\) None 0 12
3528.1.fv \(\chi_{3528}(143, \cdot)\) None 0 12
3528.1.fw \(\chi_{3528}(409, \cdot)\) None 0 12
3528.1.fx \(\chi_{3528}(331, \cdot)\) None 0 12
3528.1.gc \(\chi_{3528}(65, \cdot)\) None 0 12
3528.1.gd \(\chi_{3528}(59, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3528))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3528)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 27}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1764))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3528))\)\(^{\oplus 1}\)