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Properties

Label 5203.2
Level 5203
Weight 2
Dimension 1092688
Nonzero newspaces 32
Sturm bound 4472160

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Defining parameters

Level: \( N \) = \( 5203 = 11^{2} \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(4472160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5203))\).

Total New Old
Modular forms 1124760 1104208 20552
Cusp forms 1111321 1092688 18633
Eisenstein series 13439 11520 1919

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5203))\)

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
5203.2.a \(\chi_{5203}(1, \cdot)\) 5203.2.a.a 1 1
5203.2.a.b 1
5203.2.a.c 2
5203.2.a.d 2
5203.2.a.e 2
5203.2.a.f 2
5203.2.a.g 2
5203.2.a.h 5
5203.2.a.i 5
5203.2.a.j 9
5203.2.a.k 11
5203.2.a.l 15
5203.2.a.m 15
5203.2.a.n 17
5203.2.a.o 17
5203.2.a.p 18
5203.2.a.q 18
5203.2.a.r 36
5203.2.a.s 36
5203.2.a.t 38
5203.2.a.u 38
5203.2.a.v 46
5203.2.a.w 46
5203.2.d \(\chi_{5203}(5202, \cdot)\) n/a 388 1
5203.2.e \(\chi_{5203}(122, \cdot)\) n/a 782 2
5203.2.f \(\chi_{5203}(130, \cdot)\) n/a 1512 4
5203.2.i \(\chi_{5203}(725, \cdot)\) n/a 776 2
5203.2.j \(\chi_{5203}(606, \cdot)\) n/a 2340 6
5203.2.k \(\chi_{5203}(3482, \cdot)\) n/a 1552 4
5203.2.n \(\chi_{5203}(474, \cdot)\) n/a 4620 10
5203.2.o \(\chi_{5203}(604, \cdot)\) n/a 2328 6
5203.2.r \(\chi_{5203}(251, \cdot)\) n/a 3104 8
5203.2.s \(\chi_{5203}(848, \cdot)\) n/a 4692 12
5203.2.t \(\chi_{5203}(472, \cdot)\) n/a 4820 10
5203.2.w \(\chi_{5203}(596, \cdot)\) n/a 3104 8
5203.2.z \(\chi_{5203}(221, \cdot)\) n/a 9640 20
5203.2.ba \(\chi_{5203}(269, \cdot)\) n/a 9312 24
5203.2.bb \(\chi_{5203}(120, \cdot)\) n/a 4656 12
5203.2.be \(\chi_{5203}(302, \cdot)\) n/a 18480 40
5203.2.bf \(\chi_{5203}(252, \cdot)\) n/a 9640 20
5203.2.bk \(\chi_{5203}(94, \cdot)\) n/a 9312 24
5203.2.bl \(\chi_{5203}(78, \cdot)\) n/a 28920 60
5203.2.bm \(\chi_{5203}(9, \cdot)\) n/a 18624 48
5203.2.bp \(\chi_{5203}(85, \cdot)\) n/a 19280 40
5203.2.bs \(\chi_{5203}(32, \cdot)\) n/a 28920 60
5203.2.bt \(\chi_{5203}(36, \cdot)\) n/a 38560 80
5203.2.bw \(\chi_{5203}(112, \cdot)\) n/a 18624 48
5203.2.bx \(\chi_{5203}(23, \cdot)\) n/a 57840 120
5203.2.ca \(\chi_{5203}(7, \cdot)\) n/a 38560 80
5203.2.cb \(\chi_{5203}(4, \cdot)\) n/a 115680 240
5203.2.ce \(\chi_{5203}(76, \cdot)\) n/a 57840 120
5203.2.cf \(\chi_{5203}(2, \cdot)\) n/a 115680 240
5203.2.ci \(\chi_{5203}(14, \cdot)\) n/a 231360 480
5203.2.cj \(\chi_{5203}(18, \cdot)\) n/a 231360 480

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5203))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5203)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(473))\)\(^{\oplus 2}\)