Properties

Label 5780.2
Level 5780
Weight 2
Dimension 528171
Nonzero newspaces 36
Sturm bound 3995136

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 5780 = 2^{2} \cdot 5 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(3995136\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5780))\).

Total New Old
Modular forms 1006784 532595 474189
Cusp forms 990785 528171 462614
Eisenstein series 15999 4424 11575

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5780))\)

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
5780.2.a \(\chi_{5780}(1, \cdot)\) 5780.2.a.a 1 1
5780.2.a.b 1
5780.2.a.c 1
5780.2.a.d 1
5780.2.a.e 1
5780.2.a.f 1
5780.2.a.g 2
5780.2.a.h 2
5780.2.a.i 3
5780.2.a.j 3
5780.2.a.k 3
5780.2.a.l 6
5780.2.a.m 6
5780.2.a.n 6
5780.2.a.o 6
5780.2.a.p 12
5780.2.a.q 12
5780.2.a.r 12
5780.2.a.s 12
5780.2.c \(\chi_{5780}(5201, \cdot)\) 5780.2.c.a 2 1
5780.2.c.b 2
5780.2.c.c 2
5780.2.c.d 2
5780.2.c.e 4
5780.2.c.f 6
5780.2.c.g 12
5780.2.c.h 12
5780.2.c.i 24
5780.2.c.j 24
5780.2.e \(\chi_{5780}(3469, \cdot)\) n/a 136 1
5780.2.g \(\chi_{5780}(2889, \cdot)\) n/a 136 1
5780.2.i \(\chi_{5780}(1407, \cdot)\) n/a 1564 2
5780.2.l \(\chi_{5780}(4047, \cdot)\) n/a 1566 2
5780.2.m \(\chi_{5780}(829, \cdot)\) n/a 272 2
5780.2.o \(\chi_{5780}(2061, \cdot)\) n/a 180 2
5780.2.r \(\chi_{5780}(3467, \cdot)\) n/a 1564 2
5780.2.s \(\chi_{5780}(327, \cdot)\) n/a 1564 2
5780.2.u \(\chi_{5780}(1001, \cdot)\) n/a 360 4
5780.2.w \(\chi_{5780}(423, \cdot)\) n/a 3128 4
5780.2.z \(\chi_{5780}(2467, \cdot)\) n/a 3128 4
5780.2.bb \(\chi_{5780}(1889, \cdot)\) n/a 536 4
5780.2.bd \(\chi_{5780}(513, \cdot)\) n/a 1080 8
5780.2.bf \(\chi_{5780}(131, \cdot)\) n/a 4320 8
5780.2.bg \(\chi_{5780}(1659, \cdot)\) n/a 6256 8
5780.2.bi \(\chi_{5780}(653, \cdot)\) n/a 1080 8
5780.2.bk \(\chi_{5780}(341, \cdot)\) n/a 1632 16
5780.2.bm \(\chi_{5780}(169, \cdot)\) n/a 2432 16
5780.2.bo \(\chi_{5780}(69, \cdot)\) n/a 2432 16
5780.2.bq \(\chi_{5780}(101, \cdot)\) n/a 1632 16
5780.2.bt \(\chi_{5780}(183, \cdot)\) n/a 29248 32
5780.2.bu \(\chi_{5780}(67, \cdot)\) n/a 29248 32
5780.2.bx \(\chi_{5780}(21, \cdot)\) n/a 3264 32
5780.2.bz \(\chi_{5780}(89, \cdot)\) n/a 4864 32
5780.2.ca \(\chi_{5780}(103, \cdot)\) n/a 29248 32
5780.2.cd \(\chi_{5780}(47, \cdot)\) n/a 29248 32
5780.2.ce \(\chi_{5780}(9, \cdot)\) n/a 9856 64
5780.2.cg \(\chi_{5780}(43, \cdot)\) n/a 58496 64
5780.2.cj \(\chi_{5780}(83, \cdot)\) n/a 58496 64
5780.2.cl \(\chi_{5780}(121, \cdot)\) n/a 6528 64
5780.2.cn \(\chi_{5780}(37, \cdot)\) n/a 19584 128
5780.2.cp \(\chi_{5780}(39, \cdot)\) n/a 116992 128
5780.2.cq \(\chi_{5780}(11, \cdot)\) n/a 78336 128
5780.2.cs \(\chi_{5780}(57, \cdot)\) n/a 19584 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5780))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5780)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1445))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2890))\)\(^{\oplus 2}\)