Properties

Label 900.6
Level 900
Weight 6
Dimension 45783
Nonzero newspaces 24
Sturm bound 259200
Trace bound 16

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Defining parameters

Level: \( N \) = \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(259200\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(900))\).

Total New Old
Modular forms 109120 46151 62969
Cusp forms 106880 45783 61097
Eisenstein series 2240 368 1872

Trace form

\( 45783 q - 21 q^{2} + 12 q^{3} - 43 q^{4} - 67 q^{5} - 67 q^{6} + 93 q^{7} - 510 q^{8} - 266 q^{9} - 640 q^{10} + 1877 q^{11} - 510 q^{12} - 1187 q^{13} - 1524 q^{14} - 2172 q^{15} - 6159 q^{16} - 756 q^{17}+ \cdots + 694537 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(900))\)

We only show spaces with even 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
900.6.a \(\chi_{900}(1, \cdot)\) 900.6.a.a 1 1
900.6.a.b 1
900.6.a.c 1
900.6.a.d 1
900.6.a.e 1
900.6.a.f 1
900.6.a.g 1
900.6.a.h 1
900.6.a.i 1
900.6.a.j 1
900.6.a.k 1
900.6.a.l 2
900.6.a.m 2
900.6.a.n 2
900.6.a.o 2
900.6.a.p 2
900.6.a.q 2
900.6.a.r 2
900.6.a.s 2
900.6.a.t 2
900.6.a.u 2
900.6.a.v 2
900.6.a.w 3
900.6.a.x 3
900.6.d \(\chi_{900}(649, \cdot)\) 900.6.d.a 2 1
900.6.d.b 2
900.6.d.c 2
900.6.d.d 2
900.6.d.e 2
900.6.d.f 2
900.6.d.g 2
900.6.d.h 2
900.6.d.i 2
900.6.d.j 4
900.6.d.k 4
900.6.d.l 4
900.6.d.m 4
900.6.d.n 4
900.6.e \(\chi_{900}(251, \cdot)\) n/a 190 1
900.6.h \(\chi_{900}(899, \cdot)\) n/a 180 1
900.6.i \(\chi_{900}(301, \cdot)\) n/a 190 2
900.6.j \(\chi_{900}(557, \cdot)\) 900.6.j.a 16 2
900.6.j.b 20
900.6.j.c 24
900.6.k \(\chi_{900}(307, \cdot)\) n/a 446 2
900.6.n \(\chi_{900}(181, \cdot)\) n/a 252 4
900.6.o \(\chi_{900}(299, \cdot)\) n/a 1072 2
900.6.r \(\chi_{900}(551, \cdot)\) n/a 1128 2
900.6.s \(\chi_{900}(49, \cdot)\) n/a 180 2
900.6.v \(\chi_{900}(71, \cdot)\) n/a 1200 4
900.6.w \(\chi_{900}(109, \cdot)\) n/a 248 4
900.6.z \(\chi_{900}(179, \cdot)\) n/a 1200 4
900.6.be \(\chi_{900}(257, \cdot)\) n/a 360 4
900.6.bf \(\chi_{900}(7, \cdot)\) n/a 2144 4
900.6.bg \(\chi_{900}(61, \cdot)\) n/a 1200 8
900.6.bj \(\chi_{900}(127, \cdot)\) n/a 2984 8
900.6.bk \(\chi_{900}(17, \cdot)\) n/a 400 8
900.6.bn \(\chi_{900}(59, \cdot)\) n/a 7168 8
900.6.bq \(\chi_{900}(169, \cdot)\) n/a 1200 8
900.6.br \(\chi_{900}(11, \cdot)\) n/a 7168 8
900.6.bs \(\chi_{900}(67, \cdot)\) n/a 14336 16
900.6.bt \(\chi_{900}(77, \cdot)\) n/a 2400 16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(900))\) into lower level spaces

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