Properties

Label 900.1
Level 900
Weight 1
Dimension 50
Nonzero newspaces 8
Newforms 9
Sturm bound 43200
Trace bound 13

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Defining parameters

Level: \( N \) = \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newforms: \( 9 \)
Sturm bound: \(43200\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(900))\).

Total New Old
Modular forms 1224 235 989
Cusp forms 104 50 54
Eisenstein series 1120 185 935

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 50 0 0 0

Trace form

\(50q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut -\mathstrut 15q^{34} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut q^{37} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut -\mathstrut 8q^{41} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut -\mathstrut 10q^{52} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut +\mathstrut 2q^{54} \) \(\mathstrut +\mathstrut 14q^{56} \) \(\mathstrut -\mathstrut 10q^{58} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 6q^{82} \) \(\mathstrut -\mathstrut 2q^{84} \) \(\mathstrut -\mathstrut 11q^{85} \) \(\mathstrut -\mathstrut 4q^{86} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut -\mathstrut 2q^{94} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut -\mathstrut 10q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(900))\)

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
900.1.b \(\chi_{900}(449, \cdot)\) None 0 1
900.1.c \(\chi_{900}(451, \cdot)\) 900.1.c.a 1 1
900.1.c.b 1
900.1.f \(\chi_{900}(199, \cdot)\) None 0 1
900.1.g \(\chi_{900}(701, \cdot)\) None 0 1
900.1.l \(\chi_{900}(757, \cdot)\) 900.1.l.a 4 2
900.1.m \(\chi_{900}(107, \cdot)\) 900.1.m.a 4 2
900.1.p \(\chi_{900}(101, \cdot)\) None 0 2
900.1.q \(\chi_{900}(499, \cdot)\) None 0 2
900.1.t \(\chi_{900}(151, \cdot)\) 900.1.t.a 4 2
900.1.u \(\chi_{900}(149, \cdot)\) None 0 2
900.1.x \(\chi_{900}(91, \cdot)\) 900.1.x.a 4 4
900.1.y \(\chi_{900}(89, \cdot)\) None 0 4
900.1.ba \(\chi_{900}(161, \cdot)\) None 0 4
900.1.bb \(\chi_{900}(19, \cdot)\) 900.1.bb.a 8 4
900.1.bc \(\chi_{900}(157, \cdot)\) None 0 4
900.1.bd \(\chi_{900}(407, \cdot)\) 900.1.bd.a 8 4
900.1.bh \(\chi_{900}(287, \cdot)\) 900.1.bh.a 16 8
900.1.bi \(\chi_{900}(37, \cdot)\) None 0 8
900.1.bl \(\chi_{900}(79, \cdot)\) None 0 8
900.1.bm \(\chi_{900}(41, \cdot)\) None 0 8
900.1.bo \(\chi_{900}(29, \cdot)\) None 0 8
900.1.bp \(\chi_{900}(31, \cdot)\) None 0 8
900.1.bu \(\chi_{900}(23, \cdot)\) None 0 16
900.1.bv \(\chi_{900}(13, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(900))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(900)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)