Properties

Label 5043.2
Level 5043
Weight 2
Dimension 702821
Nonzero newspaces 16
Sturm bound 3765440

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 5043 = 3 \cdot 41^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(3765440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5043))\).

Total New Old
Modular forms 946240 707541 238699
Cusp forms 936481 702821 233660
Eisenstein series 9759 4720 5039

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5043))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5043.2.a \(\chi_{5043}(1, \cdot)\) 5043.2.a.a 1 1
5043.2.a.b 1
5043.2.a.c 1
5043.2.a.d 1
5043.2.a.e 2
5043.2.a.f 2
5043.2.a.g 2
5043.2.a.h 2
5043.2.a.i 2
5043.2.a.j 3
5043.2.a.k 3
5043.2.a.l 3
5043.2.a.m 3
5043.2.a.n 3
5043.2.a.o 4
5043.2.a.p 4
5043.2.a.q 4
5043.2.a.r 4
5043.2.a.s 6
5043.2.a.t 6
5043.2.a.u 6
5043.2.a.v 6
5043.2.a.w 8
5043.2.a.x 8
5043.2.a.y 12
5043.2.a.z 12
5043.2.a.ba 16
5043.2.a.bb 16
5043.2.a.bc 18
5043.2.a.bd 18
5043.2.a.be 24
5043.2.a.bf 24
5043.2.a.bg 24
5043.2.a.bh 24
5043.2.d \(\chi_{5043}(3361, \cdot)\) n/a 272 1
5043.2.e \(\chi_{5043}(1303, \cdot)\) n/a 548 2
5043.2.g \(\chi_{5043}(1732, \cdot)\) n/a 1088 4
5043.2.i \(\chi_{5043}(776, \cdot)\) n/a 2032 4
5043.2.j \(\chi_{5043}(148, \cdot)\) n/a 1088 4
5043.2.n \(\chi_{5043}(487, \cdot)\) n/a 2192 8
5043.2.o \(\chi_{5043}(509, \cdot)\) n/a 8128 16
5043.2.q \(\chi_{5043}(124, \cdot)\) n/a 11520 40
5043.2.r \(\chi_{5043}(40, \cdot)\) n/a 11520 40
5043.2.v \(\chi_{5043}(73, \cdot)\) n/a 22880 80
5043.2.w \(\chi_{5043}(10, \cdot)\) n/a 46080 160
5043.2.x \(\chi_{5043}(14, \cdot)\) n/a 91520 160
5043.2.bb \(\chi_{5043}(4, \cdot)\) n/a 46080 160
5043.2.bc \(\chi_{5043}(43, \cdot)\) n/a 91520 320
5043.2.bf \(\chi_{5043}(11, \cdot)\) n/a 366080 640

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5043))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5043)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1681))\)\(^{\oplus 2}\)