Properties

Label 1800.1
Level 1800
Weight 1
Dimension 108
Nonzero newspaces 11
Newforms 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: \( 11 \)
Newforms: \( 24 \)
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

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

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 the 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

\( S_{1}^{\mathrm{old}}(\Gamma_1(1800)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 2}\)