Properties

Label 5625.2
Level 5625
Weight 2
Dimension 817344
Nonzero newspaces 24
Sturm bound 4500000

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Defining parameters

Level: \( N \) = \( 5625 = 3^{2} \cdot 5^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(4500000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5625))\).

Total New Old
Modular forms 1133800 824256 309544
Cusp forms 1116201 817344 298857
Eisenstein series 17599 6912 10687

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5625))\)

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
5625.2.a \(\chi_{5625}(1, \cdot)\) 5625.2.a.a 2 1
5625.2.a.b 2
5625.2.a.c 2
5625.2.a.d 2
5625.2.a.e 2
5625.2.a.f 2
5625.2.a.g 2
5625.2.a.h 2
5625.2.a.i 4
5625.2.a.j 4
5625.2.a.k 4
5625.2.a.l 4
5625.2.a.m 4
5625.2.a.n 4
5625.2.a.o 6
5625.2.a.p 6
5625.2.a.q 6
5625.2.a.r 6
5625.2.a.s 8
5625.2.a.t 8
5625.2.a.u 8
5625.2.a.v 8
5625.2.a.w 8
5625.2.a.x 8
5625.2.a.y 8
5625.2.a.z 8
5625.2.a.ba 8
5625.2.a.bb 8
5625.2.a.bc 8
5625.2.a.bd 8
5625.2.a.be 8
5625.2.a.bf 24
5625.2.b \(\chi_{5625}(3124, \cdot)\) n/a 192 1
5625.2.e \(\chi_{5625}(1876, \cdot)\) n/a 928 2
5625.2.f \(\chi_{5625}(3932, \cdot)\) n/a 320 2
5625.2.h \(\chi_{5625}(1126, \cdot)\) n/a 776 4
5625.2.k \(\chi_{5625}(1249, \cdot)\) n/a 928 2
5625.2.m \(\chi_{5625}(874, \cdot)\) n/a 776 4
5625.2.p \(\chi_{5625}(182, \cdot)\) n/a 1856 4
5625.2.q \(\chi_{5625}(376, \cdot)\) n/a 3744 8
5625.2.s \(\chi_{5625}(557, \cdot)\) n/a 1280 8
5625.2.t \(\chi_{5625}(226, \cdot)\) n/a 3700 20
5625.2.v \(\chi_{5625}(124, \cdot)\) n/a 3744 8
5625.2.y \(\chi_{5625}(199, \cdot)\) n/a 3680 20
5625.2.ba \(\chi_{5625}(68, \cdot)\) n/a 7488 16
5625.2.bc \(\chi_{5625}(76, \cdot)\) n/a 17760 40
5625.2.be \(\chi_{5625}(107, \cdot)\) n/a 6000 40
5625.2.bf \(\chi_{5625}(46, \cdot)\) n/a 31100 100
5625.2.bg \(\chi_{5625}(49, \cdot)\) n/a 17760 40
5625.2.bl \(\chi_{5625}(19, \cdot)\) n/a 31200 100
5625.2.bn \(\chi_{5625}(32, \cdot)\) n/a 35520 80
5625.2.bo \(\chi_{5625}(16, \cdot)\) n/a 149600 200
5625.2.bq \(\chi_{5625}(8, \cdot)\) n/a 50000 200
5625.2.br \(\chi_{5625}(4, \cdot)\) n/a 149600 200
5625.2.bv \(\chi_{5625}(2, \cdot)\) n/a 299200 400

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5625))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5625)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1125))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1875))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5625))\)\(^{\oplus 1}\)