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Properties

Label 2040.1
Level 2040
Weight 1
Dimension 96
Nonzero newspaces 4
Newform subspaces 18
Sturm bound 221184
Trace bound 6

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Defining parameters

Level: \( N \) = \( 2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 18 \)
Sturm bound: \(221184\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2040))\).

Total New Old
Modular forms 3528 456 3072
Cusp forms 456 96 360
Eisenstein series 3072 360 2712

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 96 0 0 0

Trace form

\( 96 q - 4 q^{4} + 4 q^{6} - 8 q^{9} + O(q^{10}) \) \( 96 q - 4 q^{4} + 4 q^{6} - 8 q^{9} - 4 q^{10} - 4 q^{15} - 12 q^{16} - 4 q^{24} - 8 q^{25} - 8 q^{30} + 32 q^{31} - 8 q^{34} - 4 q^{36} + 24 q^{39} + 4 q^{40} - 8 q^{46} + 8 q^{49} - 4 q^{54} + 4 q^{60} + 8 q^{64} - 4 q^{66} - 12 q^{70} - 12 q^{76} - 16 q^{79} - 12 q^{84} + 4 q^{90} - 12 q^{94} + 4 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2040))\)

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
2040.1.b \(\chi_{2040}(101, \cdot)\) None 0 1
2040.1.d \(\chi_{2040}(1769, \cdot)\) None 0 1
2040.1.g \(\chi_{2040}(511, \cdot)\) None 0 1
2040.1.i \(\chi_{2040}(1699, \cdot)\) None 0 1
2040.1.j \(\chi_{2040}(679, \cdot)\) None 0 1
2040.1.l \(\chi_{2040}(1531, \cdot)\) None 0 1
2040.1.o \(\chi_{2040}(749, \cdot)\) None 0 1
2040.1.q \(\chi_{2040}(1121, \cdot)\) None 0 1
2040.1.s \(\chi_{2040}(919, \cdot)\) None 0 1
2040.1.u \(\chi_{2040}(1291, \cdot)\) None 0 1
2040.1.v \(\chi_{2040}(509, \cdot)\) 2040.1.v.a 1 1
2040.1.v.b 1
2040.1.v.c 1
2040.1.v.d 1
2040.1.v.e 2
2040.1.v.f 2
2040.1.v.g 4
2040.1.v.h 4
2040.1.x \(\chi_{2040}(1361, \cdot)\) None 0 1
2040.1.ba \(\chi_{2040}(341, \cdot)\) None 0 1
2040.1.bc \(\chi_{2040}(1529, \cdot)\) None 0 1
2040.1.bd \(\chi_{2040}(271, \cdot)\) None 0 1
2040.1.bf \(\chi_{2040}(1939, \cdot)\) None 0 1
2040.1.bh \(\chi_{2040}(47, \cdot)\) None 0 2
2040.1.bi \(\chi_{2040}(13, \cdot)\) None 0 2
2040.1.bl \(\chi_{2040}(803, \cdot)\) None 0 2
2040.1.bm \(\chi_{2040}(1033, \cdot)\) None 0 2
2040.1.bo \(\chi_{2040}(443, \cdot)\) None 0 2
2040.1.bq \(\chi_{2040}(577, \cdot)\) None 0 2
2040.1.bt \(\chi_{2040}(407, \cdot)\) None 0 2
2040.1.bv \(\chi_{2040}(613, \cdot)\) None 0 2
2040.1.bw \(\chi_{2040}(931, \cdot)\) None 0 2
2040.1.bz \(\chi_{2040}(89, \cdot)\) None 0 2
2040.1.cb \(\chi_{2040}(319, \cdot)\) None 0 2
2040.1.cc \(\chi_{2040}(701, \cdot)\) None 0 2
2040.1.ce \(\chi_{2040}(761, \cdot)\) None 0 2
2040.1.ch \(\chi_{2040}(259, \cdot)\) None 0 2
2040.1.cj \(\chi_{2040}(149, \cdot)\) 2040.1.cj.a 4 2
2040.1.cj.b 4
2040.1.cj.c 4
2040.1.cj.d 4
2040.1.ck \(\chi_{2040}(871, \cdot)\) None 0 2
2040.1.cn \(\chi_{2040}(817, \cdot)\) None 0 2
2040.1.cp \(\chi_{2040}(203, \cdot)\) None 0 2
2040.1.cq \(\chi_{2040}(373, \cdot)\) None 0 2
2040.1.cs \(\chi_{2040}(647, \cdot)\) None 0 2
2040.1.cv \(\chi_{2040}(973, \cdot)\) None 0 2
2040.1.cw \(\chi_{2040}(863, \cdot)\) None 0 2
2040.1.cz \(\chi_{2040}(217, \cdot)\) None 0 2
2040.1.da \(\chi_{2040}(1883, \cdot)\) None 0 2
2040.1.dc \(\chi_{2040}(19, \cdot)\) None 0 4
2040.1.df \(\chi_{2040}(389, \cdot)\) 2040.1.df.a 8 4
2040.1.df.b 8
2040.1.df.c 8
2040.1.df.d 8
2040.1.dg \(\chi_{2040}(151, \cdot)\) None 0 4
2040.1.dj \(\chi_{2040}(161, \cdot)\) None 0 4
2040.1.do \(\chi_{2040}(1103, \cdot)\) None 0 4
2040.1.dp \(\chi_{2040}(1283, \cdot)\) None 0 4
2040.1.dq \(\chi_{2040}(253, \cdot)\) None 0 4
2040.1.dr \(\chi_{2040}(433, \cdot)\) None 0 4
2040.1.ds \(\chi_{2040}(1453, \cdot)\) None 0 4
2040.1.dt \(\chi_{2040}(1273, \cdot)\) None 0 4
2040.1.du \(\chi_{2040}(263, \cdot)\) None 0 4
2040.1.dv \(\chi_{2040}(83, \cdot)\) None 0 4
2040.1.eb \(\chi_{2040}(569, \cdot)\) None 0 4
2040.1.ec \(\chi_{2040}(559, \cdot)\) None 0 4
2040.1.ef \(\chi_{2040}(461, \cdot)\) None 0 4
2040.1.eg \(\chi_{2040}(331, \cdot)\) None 0 4
2040.1.ej \(\chi_{2040}(7, \cdot)\) None 0 8
2040.1.el \(\chi_{2040}(233, \cdot)\) None 0 8
2040.1.em \(\chi_{2040}(437, \cdot)\) None 0 8
2040.1.eo \(\chi_{2040}(163, \cdot)\) None 0 8
2040.1.eq \(\chi_{2040}(11, \cdot)\) None 0 8
2040.1.et \(\chi_{2040}(241, \cdot)\) None 0 8
2040.1.eu \(\chi_{2040}(109, \cdot)\) None 0 8
2040.1.ex \(\chi_{2040}(479, \cdot)\) None 0 8
2040.1.ey \(\chi_{2040}(649, \cdot)\) None 0 8
2040.1.fb \(\chi_{2040}(299, \cdot)\) 2040.1.fb.a 16 8
2040.1.fb.b 16
2040.1.fc \(\chi_{2040}(71, \cdot)\) None 0 8
2040.1.ff \(\chi_{2040}(61, \cdot)\) None 0 8
2040.1.fh \(\chi_{2040}(173, \cdot)\) None 0 8
2040.1.fj \(\chi_{2040}(403, \cdot)\) None 0 8
2040.1.fk \(\chi_{2040}(607, \cdot)\) None 0 8
2040.1.fm \(\chi_{2040}(113, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2040))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2040)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(510))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1020))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2040))\)\(^{\oplus 1}\)