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Properties

Label 5243.2
Level 5243
Weight 2
Dimension 1071310
Nonzero newspaces 16
Sturm bound 4487616

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Defining parameters

Level: \( N \) = \( 5243 = 7^{2} \cdot 107 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(4487616\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5243))\).

Total New Old
Modular forms 1128264 1081494 46770
Cusp forms 1115545 1071310 44235
Eisenstein series 12719 10184 2535

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5243))\)

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
5243.2.a \(\chi_{5243}(1, \cdot)\) 5243.2.a.a 1 1
5243.2.a.b 2
5243.2.a.c 4
5243.2.a.d 4
5243.2.a.e 6
5243.2.a.f 6
5243.2.a.g 7
5243.2.a.h 10
5243.2.a.i 12
5243.2.a.j 14
5243.2.a.k 20
5243.2.a.l 32
5243.2.a.m 35
5243.2.a.n 35
5243.2.a.o 35
5243.2.a.p 35
5243.2.a.q 38
5243.2.a.r 66
5243.2.b \(\chi_{5243}(5242, \cdot)\) n/a 356 1
5243.2.e \(\chi_{5243}(2676, \cdot)\) n/a 708 2
5243.2.h \(\chi_{5243}(962, \cdot)\) n/a 712 2
5243.2.i \(\chi_{5243}(750, \cdot)\) n/a 2976 6
5243.2.l \(\chi_{5243}(748, \cdot)\) n/a 3012 6
5243.2.m \(\chi_{5243}(429, \cdot)\) n/a 5928 12
5243.2.n \(\chi_{5243}(213, \cdot)\) n/a 6024 12
5243.2.q \(\chi_{5243}(99, \cdot)\) n/a 18928 52
5243.2.t \(\chi_{5243}(97, \cdot)\) n/a 18512 52
5243.2.u \(\chi_{5243}(30, \cdot)\) n/a 37024 104
5243.2.v \(\chi_{5243}(31, \cdot)\) n/a 37024 104
5243.2.y \(\chi_{5243}(29, \cdot)\) n/a 156624 312
5243.2.z \(\chi_{5243}(6, \cdot)\) n/a 156624 312
5243.2.bc \(\chi_{5243}(4, \cdot)\) n/a 313248 624
5243.2.bf \(\chi_{5243}(5, \cdot)\) n/a 313248 624

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5243))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5243)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(107))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(749))\)\(^{\oplus 2}\)