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Properties

Label 5776.2
Level 5776
Weight 2
Dimension 579476
Nonzero newspaces 24
Sturm bound 4158720

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Defining parameters

Level: \( N \) = \( 5776 = 2^{4} \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(4158720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5776))\).

Total New Old
Modular forms 1046736 583693 463043
Cusp forms 1032625 579476 453149
Eisenstein series 14111 4217 9894

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5776))\)

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
5776.2.a \(\chi_{5776}(1, \cdot)\) 5776.2.a.a 1 1
5776.2.a.b 1
5776.2.a.c 1
5776.2.a.d 1
5776.2.a.e 1
5776.2.a.f 1
5776.2.a.g 1
5776.2.a.h 1
5776.2.a.i 1
5776.2.a.j 1
5776.2.a.k 1
5776.2.a.l 1
5776.2.a.m 1
5776.2.a.n 1
5776.2.a.o 1
5776.2.a.p 1
5776.2.a.q 1
5776.2.a.r 2
5776.2.a.s 2
5776.2.a.t 2
5776.2.a.u 2
5776.2.a.v 2
5776.2.a.w 2
5776.2.a.x 2
5776.2.a.y 2
5776.2.a.z 2
5776.2.a.ba 2
5776.2.a.bb 2
5776.2.a.bc 2
5776.2.a.bd 2
5776.2.a.be 2
5776.2.a.bf 2
5776.2.a.bg 2
5776.2.a.bh 2
5776.2.a.bi 3
5776.2.a.bj 3
5776.2.a.bk 3
5776.2.a.bl 3
5776.2.a.bm 3
5776.2.a.bn 3
5776.2.a.bo 3
5776.2.a.bp 3
5776.2.a.bq 3
5776.2.a.br 3
5776.2.a.bs 3
5776.2.a.bt 4
5776.2.a.bu 4
5776.2.a.bv 4
5776.2.a.bw 6
5776.2.a.bx 6
5776.2.a.by 6
5776.2.a.bz 6
5776.2.a.ca 8
5776.2.a.cb 8
5776.2.a.cc 8
5776.2.a.cd 9
5776.2.a.ce 9
5776.2.b \(\chi_{5776}(2887, \cdot)\) None 0 1
5776.2.c \(\chi_{5776}(2889, \cdot)\) None 0 1
5776.2.h \(\chi_{5776}(5775, \cdot)\) n/a 170 1
5776.2.i \(\chi_{5776}(1873, \cdot)\) n/a 324 2
5776.2.k \(\chi_{5776}(1445, \cdot)\) n/a 1330 2
5776.2.m \(\chi_{5776}(1443, \cdot)\) n/a 1328 2
5776.2.n \(\chi_{5776}(3679, \cdot)\) n/a 340 2
5776.2.s \(\chi_{5776}(791, \cdot)\) None 0 2
5776.2.t \(\chi_{5776}(4761, \cdot)\) None 0 2
5776.2.u \(\chi_{5776}(1137, \cdot)\) n/a 972 6
5776.2.v \(\chi_{5776}(429, \cdot)\) n/a 2656 4
5776.2.x \(\chi_{5776}(2235, \cdot)\) n/a 2656 4
5776.2.bb \(\chi_{5776}(1145, \cdot)\) None 0 6
5776.2.bd \(\chi_{5776}(1751, \cdot)\) None 0 6
5776.2.be \(\chi_{5776}(127, \cdot)\) n/a 1020 6
5776.2.bg \(\chi_{5776}(305, \cdot)\) n/a 3402 18
5776.2.bh \(\chi_{5776}(299, \cdot)\) n/a 7968 12
5776.2.bj \(\chi_{5776}(245, \cdot)\) n/a 7968 12
5776.2.bl \(\chi_{5776}(303, \cdot)\) n/a 3420 18
5776.2.bq \(\chi_{5776}(153, \cdot)\) None 0 18
5776.2.br \(\chi_{5776}(151, \cdot)\) None 0 18
5776.2.bs \(\chi_{5776}(49, \cdot)\) n/a 6804 36
5776.2.bt \(\chi_{5776}(75, \cdot)\) n/a 27288 36
5776.2.bv \(\chi_{5776}(77, \cdot)\) n/a 27288 36
5776.2.bx \(\chi_{5776}(121, \cdot)\) None 0 36
5776.2.by \(\chi_{5776}(103, \cdot)\) None 0 36
5776.2.cd \(\chi_{5776}(31, \cdot)\) n/a 6840 36
5776.2.ce \(\chi_{5776}(17, \cdot)\) n/a 20412 108
5776.2.cg \(\chi_{5776}(27, \cdot)\) n/a 54576 72
5776.2.ci \(\chi_{5776}(45, \cdot)\) n/a 54576 72
5776.2.ck \(\chi_{5776}(15, \cdot)\) n/a 20520 108
5776.2.cl \(\chi_{5776}(71, \cdot)\) None 0 108
5776.2.cn \(\chi_{5776}(9, \cdot)\) None 0 108
5776.2.cr \(\chi_{5776}(5, \cdot)\) n/a 163728 216
5776.2.ct \(\chi_{5776}(3, \cdot)\) n/a 163728 216

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5776))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5776)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1444))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2888))\)\(^{\oplus 2}\)