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Properties

Label 1800.1
Level 1800
Weight 1
Dimension 108
Nonzero newspaces 11
Newform subspaces 24
Sturm bound 172800
Trace bound 19

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Defining parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 24 \)
Sturm bound: \(172800\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1800))\).

Total New Old
Modular forms 3098 477 2621
Cusp forms 410 108 302
Eisenstein series 2688 369 2319

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 84 0 8 16

Trace form

\( 108 q + q^{2} + 5 q^{3} - 3 q^{4} + q^{6} + 8 q^{7} - 2 q^{8} - 3 q^{9} + O(q^{10}) \) \( 108 q + q^{2} + 5 q^{3} - 3 q^{4} + q^{6} + 8 q^{7} - 2 q^{8} - 3 q^{9} + 9 q^{11} - 2 q^{14} - 3 q^{16} - 2 q^{17} - 2 q^{18} + 2 q^{19} - 9 q^{22} + q^{24} - 2 q^{25} - 8 q^{26} + 2 q^{27} - 12 q^{28} + 16 q^{30} + 16 q^{31} + q^{32} + 3 q^{33} - q^{34} + 4 q^{35} - q^{36} - q^{38} - 8 q^{40} + 7 q^{41} + 2 q^{42} - 9 q^{43} - 6 q^{44} - 16 q^{46} - q^{48} + 3 q^{49} - 17 q^{51} + q^{54} + 4 q^{55} + 2 q^{56} - 17 q^{57} + 4 q^{58} - q^{59} + 8 q^{61} - 4 q^{62} + 4 q^{65} - 22 q^{66} + 5 q^{67} + 7 q^{68} + 4 q^{70} + q^{72} - 6 q^{73} + 2 q^{75} - q^{76} - 12 q^{78} - 3 q^{81} + 2 q^{82} + 6 q^{83} - 33 q^{86} - 9 q^{88} - 8 q^{89} + 4 q^{90} - 2 q^{96} - 13 q^{97} - 2 q^{98} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1800))\)

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
1800.1.c \(\chi_{1800}(449, \cdot)\) 1800.1.c.a 4 1
1800.1.e \(\chi_{1800}(1351, \cdot)\) None 0 1
1800.1.g \(\chi_{1800}(451, \cdot)\) 1800.1.g.a 1 1
1800.1.g.b 1
1800.1.g.c 2
1800.1.i \(\chi_{1800}(1349, \cdot)\) None 0 1
1800.1.j \(\chi_{1800}(199, \cdot)\) None 0 1
1800.1.l \(\chi_{1800}(1601, \cdot)\) 1800.1.l.a 2 1
1800.1.l.b 2
1800.1.n \(\chi_{1800}(701, \cdot)\) None 0 1
1800.1.p \(\chi_{1800}(1099, \cdot)\) 1800.1.p.a 2 1
1800.1.r \(\chi_{1800}(107, \cdot)\) 1800.1.r.a 4 2
1800.1.r.b 4
1800.1.u \(\chi_{1800}(757, \cdot)\) 1800.1.u.a 4 2
1800.1.u.b 4
1800.1.v \(\chi_{1800}(793, \cdot)\) None 0 2
1800.1.y \(\chi_{1800}(143, \cdot)\) None 0 2
1800.1.ba \(\chi_{1800}(499, \cdot)\) 1800.1.ba.a 4 2
1800.1.ba.b 4
1800.1.ba.c 4
1800.1.bb \(\chi_{1800}(101, \cdot)\) None 0 2
1800.1.bd \(\chi_{1800}(401, \cdot)\) None 0 2
1800.1.bf \(\chi_{1800}(799, \cdot)\) None 0 2
1800.1.bi \(\chi_{1800}(149, \cdot)\) None 0 2
1800.1.bk \(\chi_{1800}(1051, \cdot)\) 1800.1.bk.a 2 2
1800.1.bk.b 2
1800.1.bk.c 2
1800.1.bk.d 2
1800.1.bk.e 2
1800.1.bm \(\chi_{1800}(151, \cdot)\) None 0 2
1800.1.bo \(\chi_{1800}(1049, \cdot)\) None 0 2
1800.1.bp \(\chi_{1800}(269, \cdot)\) None 0 4
1800.1.br \(\chi_{1800}(91, \cdot)\) None 0 4
1800.1.bt \(\chi_{1800}(271, \cdot)\) None 0 4
1800.1.bv \(\chi_{1800}(89, \cdot)\) None 0 4
1800.1.bx \(\chi_{1800}(19, \cdot)\) None 0 4
1800.1.bz \(\chi_{1800}(341, \cdot)\) None 0 4
1800.1.cb \(\chi_{1800}(161, \cdot)\) None 0 4
1800.1.cd \(\chi_{1800}(559, \cdot)\) None 0 4
1800.1.cf \(\chi_{1800}(193, \cdot)\) None 0 4
1800.1.cg \(\chi_{1800}(407, \cdot)\) None 0 4
1800.1.cj \(\chi_{1800}(443, \cdot)\) 1800.1.cj.a 8 4
1800.1.cj.b 8
1800.1.cj.c 8
1800.1.ck \(\chi_{1800}(157, \cdot)\) None 0 4
1800.1.cn \(\chi_{1800}(287, \cdot)\) None 0 8
1800.1.cq \(\chi_{1800}(73, \cdot)\) None 0 8
1800.1.cr \(\chi_{1800}(37, \cdot)\) 1800.1.cr.a 16 8
1800.1.cu \(\chi_{1800}(323, \cdot)\) None 0 8
1800.1.cw \(\chi_{1800}(79, \cdot)\) None 0 8
1800.1.cy \(\chi_{1800}(41, \cdot)\) None 0 8
1800.1.da \(\chi_{1800}(221, \cdot)\) None 0 8
1800.1.db \(\chi_{1800}(139, \cdot)\) None 0 8
1800.1.dc \(\chi_{1800}(209, \cdot)\) None 0 8
1800.1.de \(\chi_{1800}(31, \cdot)\) None 0 8
1800.1.dg \(\chi_{1800}(211, \cdot)\) 1800.1.dg.a 16 8
1800.1.di \(\chi_{1800}(29, \cdot)\) None 0 8
1800.1.dl \(\chi_{1800}(13, \cdot)\) None 0 16
1800.1.dm \(\chi_{1800}(83, \cdot)\) None 0 16
1800.1.dp \(\chi_{1800}(23, \cdot)\) None 0 16
1800.1.dq \(\chi_{1800}(97, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1800))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1800)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 27}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1800))\)\(^{\oplus 1}\)