Properties

Label 1200.1
Level 1200
Weight 1
Dimension 28
Nonzero newspaces 6
Newforms 10
Sturm bound 76800
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 10 \)
Sturm bound: \(76800\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1200))\).

Total New Old
Modular forms 1750 213 1537
Cusp forms 182 28 154
Eisenstein series 1568 185 1383

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 28 0 0 0

Trace form

\(28q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 4q^{34} \) \(\mathstrut -\mathstrut 12q^{36} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 4q^{54} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1200))\)

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
1200.1.c \(\chi_{1200}(449, \cdot)\) 1200.1.c.a 2 1
1200.1.e \(\chi_{1200}(751, \cdot)\) None 0 1
1200.1.g \(\chi_{1200}(151, \cdot)\) None 0 1
1200.1.i \(\chi_{1200}(1049, \cdot)\) None 0 1
1200.1.j \(\chi_{1200}(799, \cdot)\) None 0 1
1200.1.l \(\chi_{1200}(401, \cdot)\) 1200.1.l.a 1 1
1200.1.l.b 1
1200.1.n \(\chi_{1200}(1001, \cdot)\) None 0 1
1200.1.p \(\chi_{1200}(199, \cdot)\) None 0 1
1200.1.q \(\chi_{1200}(499, \cdot)\) None 0 2
1200.1.r \(\chi_{1200}(101, \cdot)\) 1200.1.r.a 4 2
1200.1.u \(\chi_{1200}(407, \cdot)\) None 0 2
1200.1.x \(\chi_{1200}(457, \cdot)\) None 0 2
1200.1.z \(\chi_{1200}(107, \cdot)\) 1200.1.z.a 2 2
1200.1.z.b 2
1200.1.ba \(\chi_{1200}(493, \cdot)\) None 0 2
1200.1.bd \(\chi_{1200}(443, \cdot)\) 1200.1.bd.a 2 2
1200.1.bd.b 2
1200.1.be \(\chi_{1200}(157, \cdot)\) None 0 2
1200.1.bg \(\chi_{1200}(193, \cdot)\) None 0 2
1200.1.bj \(\chi_{1200}(143, \cdot)\) 1200.1.bj.a 4 2
1200.1.bj.b 8
1200.1.bm \(\chi_{1200}(149, \cdot)\) None 0 2
1200.1.bn \(\chi_{1200}(451, \cdot)\) None 0 2
1200.1.bp \(\chi_{1200}(89, \cdot)\) None 0 4
1200.1.br \(\chi_{1200}(391, \cdot)\) None 0 4
1200.1.bt \(\chi_{1200}(31, \cdot)\) None 0 4
1200.1.bv \(\chi_{1200}(209, \cdot)\) None 0 4
1200.1.bx \(\chi_{1200}(439, \cdot)\) None 0 4
1200.1.bz \(\chi_{1200}(41, \cdot)\) None 0 4
1200.1.cb \(\chi_{1200}(161, \cdot)\) None 0 4
1200.1.cd \(\chi_{1200}(79, \cdot)\) None 0 4
1200.1.cg \(\chi_{1200}(221, \cdot)\) None 0 8
1200.1.ch \(\chi_{1200}(19, \cdot)\) None 0 8
1200.1.ci \(\chi_{1200}(47, \cdot)\) None 0 8
1200.1.cl \(\chi_{1200}(97, \cdot)\) None 0 8
1200.1.cn \(\chi_{1200}(133, \cdot)\) None 0 8
1200.1.co \(\chi_{1200}(203, \cdot)\) None 0 8
1200.1.cr \(\chi_{1200}(13, \cdot)\) None 0 8
1200.1.cs \(\chi_{1200}(83, \cdot)\) None 0 8
1200.1.cu \(\chi_{1200}(73, \cdot)\) None 0 8
1200.1.cx \(\chi_{1200}(23, \cdot)\) None 0 8
1200.1.cy \(\chi_{1200}(91, \cdot)\) None 0 8
1200.1.cz \(\chi_{1200}(29, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1200))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1200)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 2}\)