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Properties

Label 5202.2
Level 5202
Weight 2
Dimension 196310
Nonzero newspaces 20
Sturm bound 2996352

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Defining parameters

Level: \( N \) = \( 5202 = 2 \cdot 3^{2} \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(2996352\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5202))\).

Total New Old
Modular forms 755488 196310 559178
Cusp forms 742689 196310 546379
Eisenstein series 12799 0 12799

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5202))\)

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
5202.2.a \(\chi_{5202}(1, \cdot)\) 5202.2.a.a 1 1
5202.2.a.b 1
5202.2.a.c 1
5202.2.a.d 1
5202.2.a.e 1
5202.2.a.f 1
5202.2.a.g 1
5202.2.a.h 1
5202.2.a.i 1
5202.2.a.j 1
5202.2.a.k 1
5202.2.a.l 1
5202.2.a.m 1
5202.2.a.n 1
5202.2.a.o 2
5202.2.a.p 2
5202.2.a.q 2
5202.2.a.r 2
5202.2.a.s 2
5202.2.a.t 2
5202.2.a.u 2
5202.2.a.v 2
5202.2.a.w 2
5202.2.a.x 2
5202.2.a.y 2
5202.2.a.z 2
5202.2.a.ba 2
5202.2.a.bb 2
5202.2.a.bc 2
5202.2.a.bd 2
5202.2.a.be 2
5202.2.a.bf 3
5202.2.a.bg 3
5202.2.a.bh 3
5202.2.a.bi 3
5202.2.a.bj 3
5202.2.a.bk 3
5202.2.a.bl 3
5202.2.a.bm 3
5202.2.a.bn 3
5202.2.a.bo 3
5202.2.a.bp 3
5202.2.a.bq 3
5202.2.a.br 4
5202.2.a.bs 4
5202.2.a.bt 4
5202.2.a.bu 4
5202.2.a.bv 4
5202.2.a.bw 4
5202.2.a.bx 4
5202.2.b \(\chi_{5202}(577, \cdot)\) n/a 112 1
5202.2.e \(\chi_{5202}(1735, \cdot)\) n/a 542 2
5202.2.g \(\chi_{5202}(829, \cdot)\) n/a 224 2
5202.2.j \(\chi_{5202}(2311, \cdot)\) n/a 540 2
5202.2.l \(\chi_{5202}(757, \cdot)\) n/a 452 4
5202.2.n \(\chi_{5202}(1483, \cdot)\) n/a 1080 4
5202.2.o \(\chi_{5202}(503, \cdot)\) n/a 720 8
5202.2.q \(\chi_{5202}(307, \cdot)\) n/a 2048 16
5202.2.s \(\chi_{5202}(733, \cdot)\) n/a 2160 8
5202.2.v \(\chi_{5202}(271, \cdot)\) n/a 2048 16
5202.2.w \(\chi_{5202}(65, \cdot)\) n/a 4320 16
5202.2.y \(\chi_{5202}(103, \cdot)\) n/a 9792 32
5202.2.z \(\chi_{5202}(55, \cdot)\) n/a 4096 32
5202.2.bb \(\chi_{5202}(67, \cdot)\) n/a 9792 32
5202.2.be \(\chi_{5202}(19, \cdot)\) n/a 8128 64
5202.2.bg \(\chi_{5202}(13, \cdot)\) n/a 19584 64
5202.2.bj \(\chi_{5202}(71, \cdot)\) n/a 13056 128
5202.2.bk \(\chi_{5202}(25, \cdot)\) n/a 39168 128
5202.2.bn \(\chi_{5202}(5, \cdot)\) n/a 78336 256

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5202))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5202)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1734))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2601))\)\(^{\oplus 2}\)