Properties

Label 5577.2
Level 5577
Weight 2
Dimension 823998
Nonzero newspaces 48
Sturm bound 4542720

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Defining parameters

Level: \( N \) = \( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(4542720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5577))\).

Total New Old
Modular forms 1144800 831362 313438
Cusp forms 1126561 823998 302563
Eisenstein series 18239 7364 10875

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5577))\)

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
5577.2.a \(\chi_{5577}(1, \cdot)\) 5577.2.a.a 1 1
5577.2.a.b 1
5577.2.a.c 1
5577.2.a.d 1
5577.2.a.e 1
5577.2.a.f 1
5577.2.a.g 1
5577.2.a.h 2
5577.2.a.i 2
5577.2.a.j 3
5577.2.a.k 3
5577.2.a.l 3
5577.2.a.m 4
5577.2.a.n 5
5577.2.a.o 5
5577.2.a.p 5
5577.2.a.q 5
5577.2.a.r 5
5577.2.a.s 5
5577.2.a.t 5
5577.2.a.u 5
5577.2.a.v 5
5577.2.a.w 5
5577.2.a.x 7
5577.2.a.y 7
5577.2.a.z 12
5577.2.a.ba 12
5577.2.a.bb 12
5577.2.a.bc 12
5577.2.a.bd 12
5577.2.a.be 12
5577.2.a.bf 14
5577.2.a.bg 14
5577.2.a.bh 18
5577.2.a.bi 18
5577.2.a.bj 18
5577.2.a.bk 18
5577.2.b \(\chi_{5577}(2872, \cdot)\) n/a 256 1
5577.2.e \(\chi_{5577}(5576, \cdot)\) n/a 596 1
5577.2.f \(\chi_{5577}(2705, \cdot)\) n/a 598 1
5577.2.i \(\chi_{5577}(529, \cdot)\) n/a 516 2
5577.2.j \(\chi_{5577}(2267, \cdot)\) n/a 1024 2
5577.2.m \(\chi_{5577}(3112, \cdot)\) n/a 616 2
5577.2.n \(\chi_{5577}(1015, \cdot)\) n/a 1240 4
5577.2.p \(\chi_{5577}(3233, \cdot)\) n/a 1192 2
5577.2.s \(\chi_{5577}(1882, \cdot)\) n/a 508 2
5577.2.t \(\chi_{5577}(4586, \cdot)\) n/a 1192 2
5577.2.x \(\chi_{5577}(677, \cdot)\) n/a 2392 4
5577.2.y \(\chi_{5577}(1520, \cdot)\) n/a 2384 4
5577.2.bb \(\chi_{5577}(1351, \cdot)\) n/a 1232 4
5577.2.bd \(\chi_{5577}(934, \cdot)\) n/a 1232 4
5577.2.be \(\chi_{5577}(89, \cdot)\) n/a 2056 4
5577.2.bg \(\chi_{5577}(430, \cdot)\) n/a 3600 12
5577.2.bh \(\chi_{5577}(1543, \cdot)\) n/a 2464 8
5577.2.bj \(\chi_{5577}(746, \cdot)\) n/a 4768 8
5577.2.bk \(\chi_{5577}(1084, \cdot)\) n/a 2464 8
5577.2.bo \(\chi_{5577}(131, \cdot)\) n/a 8688 12
5577.2.bp \(\chi_{5577}(428, \cdot)\) n/a 8688 12
5577.2.bs \(\chi_{5577}(298, \cdot)\) n/a 3648 12
5577.2.bu \(\chi_{5577}(530, \cdot)\) n/a 4768 8
5577.2.bv \(\chi_{5577}(361, \cdot)\) n/a 2464 8
5577.2.by \(\chi_{5577}(1205, \cdot)\) n/a 4768 8
5577.2.ca \(\chi_{5577}(100, \cdot)\) n/a 7248 24
5577.2.cb \(\chi_{5577}(109, \cdot)\) n/a 8736 24
5577.2.ce \(\chi_{5577}(122, \cdot)\) n/a 14592 24
5577.2.cf \(\chi_{5577}(19, \cdot)\) n/a 4928 16
5577.2.ci \(\chi_{5577}(80, \cdot)\) n/a 9536 16
5577.2.cj \(\chi_{5577}(157, \cdot)\) n/a 17472 48
5577.2.cl \(\chi_{5577}(296, \cdot)\) n/a 17376 24
5577.2.cm \(\chi_{5577}(166, \cdot)\) n/a 7344 24
5577.2.cp \(\chi_{5577}(230, \cdot)\) n/a 17376 24
5577.2.cr \(\chi_{5577}(25, \cdot)\) n/a 17472 48
5577.2.cu \(\chi_{5577}(116, \cdot)\) n/a 34752 48
5577.2.cv \(\chi_{5577}(248, \cdot)\) n/a 34752 48
5577.2.cz \(\chi_{5577}(254, \cdot)\) n/a 29088 48
5577.2.da \(\chi_{5577}(76, \cdot)\) n/a 17472 48
5577.2.dc \(\chi_{5577}(16, \cdot)\) n/a 34944 96
5577.2.de \(\chi_{5577}(73, \cdot)\) n/a 34944 96
5577.2.df \(\chi_{5577}(5, \cdot)\) n/a 69504 96
5577.2.di \(\chi_{5577}(29, \cdot)\) n/a 69504 96
5577.2.dl \(\chi_{5577}(4, \cdot)\) n/a 34944 96
5577.2.dm \(\chi_{5577}(17, \cdot)\) n/a 69504 96
5577.2.do \(\chi_{5577}(20, \cdot)\) n/a 139008 192
5577.2.dr \(\chi_{5577}(7, \cdot)\) n/a 69888 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5577))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5577)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1859))\)\(^{\oplus 2}\)