Properties

Label 225.6
Level 225
Weight 6
Dimension 6474
Nonzero newspaces 12
Sturm bound 21600
Trace bound 2

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Defining parameters

Level: \( N \) = \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(21600\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(225))\).

Total New Old
Modular forms 9224 6659 2565
Cusp forms 8776 6474 2302
Eisenstein series 448 185 263

Trace form

\( 6474 q - 17 q^{2} - 36 q^{3} + 37 q^{4} + 39 q^{5} + 131 q^{6} - 418 q^{7} - 1212 q^{8} - 686 q^{9} + 2300 q^{10} + 3298 q^{11} + 2188 q^{12} - 4330 q^{13} - 13782 q^{14} - 2204 q^{15} - 6935 q^{16} + 458 q^{17}+ \cdots - 2214624 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(225))\)

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
225.6.a \(\chi_{225}(1, \cdot)\) 225.6.a.a 1 1
225.6.a.b 1
225.6.a.c 1
225.6.a.d 1
225.6.a.e 1
225.6.a.f 1
225.6.a.g 1
225.6.a.h 1
225.6.a.i 2
225.6.a.j 2
225.6.a.k 2
225.6.a.l 2
225.6.a.m 2
225.6.a.n 2
225.6.a.o 2
225.6.a.p 2
225.6.a.q 2
225.6.a.r 2
225.6.a.s 2
225.6.a.t 2
225.6.a.u 2
225.6.a.v 4
225.6.b \(\chi_{225}(199, \cdot)\) 225.6.b.a 2 1
225.6.b.b 2
225.6.b.c 2
225.6.b.d 2
225.6.b.e 2
225.6.b.f 2
225.6.b.g 4
225.6.b.h 4
225.6.b.i 4
225.6.b.j 4
225.6.b.k 4
225.6.b.l 4
225.6.e \(\chi_{225}(76, \cdot)\) n/a 184 2
225.6.f \(\chi_{225}(107, \cdot)\) 225.6.f.a 16 2
225.6.f.b 20
225.6.f.c 24
225.6.h \(\chi_{225}(46, \cdot)\) n/a 244 4
225.6.k \(\chi_{225}(49, \cdot)\) n/a 176 2
225.6.m \(\chi_{225}(19, \cdot)\) n/a 248 4
225.6.p \(\chi_{225}(32, \cdot)\) n/a 352 4
225.6.q \(\chi_{225}(16, \cdot)\) n/a 1184 8
225.6.s \(\chi_{225}(8, \cdot)\) n/a 400 8
225.6.u \(\chi_{225}(4, \cdot)\) n/a 1184 8
225.6.w \(\chi_{225}(2, \cdot)\) n/a 2368 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(225))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(225)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)