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Properties

Label 1860.1
Level 1860
Weight 1
Dimension 60
Nonzero newspaces 4
Newform subspaces 16
Sturm bound 184320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 16 \)
Sturm bound: \(184320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1860))\).

Total New Old
Modular forms 2670 404 2266
Cusp forms 270 60 210
Eisenstein series 2400 344 2056

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 60 0 0 0

Trace form

\( 60 q+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1860))\)

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
1860.1.b \(\chi_{1860}(371, \cdot)\) None 0 1
1860.1.c \(\chi_{1860}(869, \cdot)\) None 0 1
1860.1.d \(\chi_{1860}(931, \cdot)\) None 0 1
1860.1.e \(\chi_{1860}(1549, \cdot)\) None 0 1
1860.1.j \(\chi_{1860}(559, \cdot)\) None 0 1
1860.1.k \(\chi_{1860}(61, \cdot)\) None 0 1
1860.1.l \(\chi_{1860}(1859, \cdot)\) 1860.1.l.a 1 1
1860.1.l.b 1
1860.1.l.c 1
1860.1.l.d 1
1860.1.m \(\chi_{1860}(1241, \cdot)\) None 0 1
1860.1.v \(\chi_{1860}(557, \cdot)\) None 0 2
1860.1.w \(\chi_{1860}(373, \cdot)\) None 0 2
1860.1.x \(\chi_{1860}(683, \cdot)\) None 0 2
1860.1.y \(\chi_{1860}(247, \cdot)\) None 0 2
1860.1.bd \(\chi_{1860}(521, \cdot)\) None 0 2
1860.1.be \(\chi_{1860}(119, \cdot)\) 1860.1.be.a 2 2
1860.1.be.b 2
1860.1.be.c 2
1860.1.be.d 2
1860.1.bf \(\chi_{1860}(181, \cdot)\) None 0 2
1860.1.bg \(\chi_{1860}(439, \cdot)\) None 0 2
1860.1.bl \(\chi_{1860}(409, \cdot)\) None 0 2
1860.1.bm \(\chi_{1860}(211, \cdot)\) None 0 2
1860.1.bn \(\chi_{1860}(149, \cdot)\) None 0 2
1860.1.bo \(\chi_{1860}(491, \cdot)\) None 0 2
1860.1.bs \(\chi_{1860}(101, \cdot)\) None 0 4
1860.1.bt \(\chi_{1860}(959, \cdot)\) 1860.1.bt.a 4 4
1860.1.bt.b 4
1860.1.bt.c 4
1860.1.bt.d 4
1860.1.bu \(\chi_{1860}(1021, \cdot)\) None 0 4
1860.1.bv \(\chi_{1860}(1039, \cdot)\) None 0 4
1860.1.ca \(\chi_{1860}(649, \cdot)\) None 0 4
1860.1.cb \(\chi_{1860}(1411, \cdot)\) None 0 4
1860.1.cc \(\chi_{1860}(1349, \cdot)\) None 0 4
1860.1.cd \(\chi_{1860}(1331, \cdot)\) None 0 4
1860.1.ce \(\chi_{1860}(223, \cdot)\) None 0 4
1860.1.cf \(\chi_{1860}(563, \cdot)\) None 0 4
1860.1.cg \(\chi_{1860}(253, \cdot)\) None 0 4
1860.1.ch \(\chi_{1860}(533, \cdot)\) None 0 4
1860.1.cn \(\chi_{1860}(463, \cdot)\) None 0 8
1860.1.co \(\chi_{1860}(47, \cdot)\) None 0 8
1860.1.cp \(\chi_{1860}(97, \cdot)\) None 0 8
1860.1.cq \(\chi_{1860}(77, \cdot)\) None 0 8
1860.1.cv \(\chi_{1860}(11, \cdot)\) None 0 8
1860.1.cw \(\chi_{1860}(329, \cdot)\) None 0 8
1860.1.cx \(\chi_{1860}(391, \cdot)\) None 0 8
1860.1.cy \(\chi_{1860}(229, \cdot)\) None 0 8
1860.1.dd \(\chi_{1860}(19, \cdot)\) None 0 8
1860.1.de \(\chi_{1860}(241, \cdot)\) None 0 8
1860.1.df \(\chi_{1860}(179, \cdot)\) 1860.1.df.a 8 8
1860.1.df.b 8
1860.1.df.c 8
1860.1.df.d 8
1860.1.dg \(\chi_{1860}(41, \cdot)\) None 0 8
1860.1.do \(\chi_{1860}(17, \cdot)\) None 0 16
1860.1.dp \(\chi_{1860}(133, \cdot)\) None 0 16
1860.1.dq \(\chi_{1860}(107, \cdot)\) None 0 16
1860.1.dr \(\chi_{1860}(43, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1860))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1860)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(930))\)\(^{\oplus 2}\)