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Properties

Label 13552.2
Level 13552
Weight 2
Dimension 2949845
Nonzero newspaces 64
Sturm bound 22302720

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Defining parameters

Level: \( N \) = \( 13552 = 2^{4} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(22302720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(13552))\).

Total New Old
Modular forms 5602560 2962489 2640071
Cusp forms 5548801 2949845 2598956
Eisenstein series 53759 12644 41115

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(13552))\)

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
13552.2.a \(\chi_{13552}(1, \cdot)\) 13552.2.a.a 1 1
13552.2.a.b 1
13552.2.a.c 1
13552.2.a.d 1
13552.2.a.e 1
13552.2.a.f 1
13552.2.a.g 1
13552.2.a.h 1
13552.2.a.i 1
13552.2.a.j 1
13552.2.a.k 1
13552.2.a.l 1
13552.2.a.m 1
13552.2.a.n 1
13552.2.a.o 1
13552.2.a.p 1
13552.2.a.q 1
13552.2.a.r 1
13552.2.a.s 1
13552.2.a.t 1
13552.2.a.u 1
13552.2.a.v 1
13552.2.a.w 1
13552.2.a.x 1
13552.2.a.y 1
13552.2.a.z 1
13552.2.a.ba 1
13552.2.a.bb 1
13552.2.a.bc 1
13552.2.a.bd 2
13552.2.a.be 2
13552.2.a.bf 2
13552.2.a.bg 2
13552.2.a.bh 2
13552.2.a.bi 2
13552.2.a.bj 2
13552.2.a.bk 2
13552.2.a.bl 2
13552.2.a.bm 2
13552.2.a.bn 2
13552.2.a.bo 2
13552.2.a.bp 2
13552.2.a.bq 2
13552.2.a.br 2
13552.2.a.bs 2
13552.2.a.bt 2
13552.2.a.bu 2
13552.2.a.bv 2
13552.2.a.bw 2
13552.2.a.bx 2
13552.2.a.by 2
13552.2.a.bz 2
13552.2.a.ca 2
13552.2.a.cb 2
13552.2.a.cc 2
13552.2.a.cd 2
13552.2.a.ce 2
13552.2.a.cf 2
13552.2.a.cg 2
13552.2.a.ch 2
13552.2.a.ci 2
13552.2.a.cj 3
13552.2.a.ck 3
13552.2.a.cl 3
13552.2.a.cm 3
13552.2.a.cn 3
13552.2.a.co 3
13552.2.a.cp 3
13552.2.a.cq 3
13552.2.a.cr 3
13552.2.a.cs 3
13552.2.a.ct 3
13552.2.a.cu 3
13552.2.a.cv 4
13552.2.a.cw 4
13552.2.a.cx 4
13552.2.a.cy 4
13552.2.a.cz 4
13552.2.a.da 4
13552.2.a.db 4
13552.2.a.dc 4
13552.2.a.dd 4
13552.2.a.de 4
13552.2.a.df 4
13552.2.a.dg 4
13552.2.a.dh 4
13552.2.a.di 5
13552.2.a.dj 5
13552.2.a.dk 6
13552.2.a.dl 6
13552.2.a.dm 6
13552.2.a.dn 6
13552.2.a.do 6
13552.2.a.dp 6
13552.2.a.dq 6
13552.2.a.dr 6
13552.2.a.ds 8
13552.2.a.dt 8
13552.2.a.du 8
13552.2.a.dv 8
13552.2.a.dw 8
13552.2.a.dx 8
13552.2.a.dy 10
13552.2.a.dz 10
13552.2.a.ea 10
13552.2.a.eb 10
13552.2.e \(\chi_{13552}(11857, \cdot)\) n/a 424 1
13552.2.f \(\chi_{13552}(7743, \cdot)\) n/a 324 1
13552.2.j \(\chi_{13552}(7503, \cdot)\) n/a 436 1
13552.2.q \(\chi_{13552}(3873, \cdot)\) n/a 854 2
13552.2.r \(\chi_{13552}(4355, \cdot)\) n/a 2592 2
13552.2.s \(\chi_{13552}(4115, \cdot)\) n/a 3452 2
13552.2.x \(\chi_{13552}(1693, \cdot)\) n/a 3424 2
13552.2.y \(\chi_{13552}(3389, \cdot)\) n/a 2616 2
13552.2.z \(\chi_{13552}(2017, \cdot)\) n/a 1296 4
13552.2.be \(\chi_{13552}(3631, \cdot)\) n/a 872 2
13552.2.bi \(\chi_{13552}(5807, \cdot)\) n/a 864 2
13552.2.bn \(\chi_{13552}(241, \cdot)\) n/a 848 2
13552.2.bv \(\chi_{13552}(1455, \cdot)\) n/a 1728 4
13552.2.bz \(\chi_{13552}(239, \cdot)\) n/a 1296 4
13552.2.ca \(\chi_{13552}(4353, \cdot)\) n/a 1696 4
13552.2.ce \(\chi_{13552}(1233, \cdot)\) n/a 3960 10
13552.2.ch \(\chi_{13552}(243, \cdot)\) n/a 6904 4
13552.2.ci \(\chi_{13552}(1451, \cdot)\) n/a 6848 4
13552.2.cj \(\chi_{13552}(485, \cdot)\) n/a 6904 4
13552.2.ck \(\chi_{13552}(3629, \cdot)\) n/a 6848 4
13552.2.cn \(\chi_{13552}(81, \cdot)\) n/a 3392 8
13552.2.co \(\chi_{13552}(4117, \cdot)\) n/a 10368 8
13552.2.cp \(\chi_{13552}(965, \cdot)\) n/a 13696 8
13552.2.cu \(\chi_{13552}(27, \cdot)\) n/a 13696 8
13552.2.cv \(\chi_{13552}(1443, \cdot)\) n/a 10368 8
13552.2.cz \(\chi_{13552}(351, \cdot)\) n/a 3960 10
13552.2.da \(\chi_{13552}(769, \cdot)\) n/a 5260 10
13552.2.dk \(\chi_{13552}(111, \cdot)\) n/a 5280 10
13552.2.dm \(\chi_{13552}(481, \cdot)\) n/a 3392 8
13552.2.dr \(\chi_{13552}(2895, \cdot)\) n/a 3456 8
13552.2.dv \(\chi_{13552}(3391, \cdot)\) n/a 3456 8
13552.2.ea \(\chi_{13552}(177, \cdot)\) n/a 10520 20
13552.2.eb \(\chi_{13552}(309, \cdot)\) n/a 31680 20
13552.2.ec \(\chi_{13552}(461, \cdot)\) n/a 42160 20
13552.2.eh \(\chi_{13552}(419, \cdot)\) n/a 42160 20
13552.2.ei \(\chi_{13552}(43, \cdot)\) n/a 31680 20
13552.2.ej \(\chi_{13552}(113, \cdot)\) n/a 15840 40
13552.2.em \(\chi_{13552}(717, \cdot)\) n/a 27392 16
13552.2.en \(\chi_{13552}(1213, \cdot)\) n/a 27392 16
13552.2.eo \(\chi_{13552}(403, \cdot)\) n/a 27392 16
13552.2.ep \(\chi_{13552}(3, \cdot)\) n/a 27392 16
13552.2.eu \(\chi_{13552}(815, \cdot)\) n/a 10560 20
13552.2.fa \(\chi_{13552}(593, \cdot)\) n/a 10520 20
13552.2.ff \(\chi_{13552}(527, \cdot)\) n/a 10560 20
13552.2.fh \(\chi_{13552}(223, \cdot)\) n/a 21120 40
13552.2.fr \(\chi_{13552}(321, \cdot)\) n/a 21040 40
13552.2.fs \(\chi_{13552}(127, \cdot)\) n/a 15840 40
13552.2.fy \(\chi_{13552}(285, \cdot)\) n/a 84320 40
13552.2.fz \(\chi_{13552}(221, \cdot)\) n/a 84320 40
13552.2.ga \(\chi_{13552}(219, \cdot)\) n/a 84320 40
13552.2.gb \(\chi_{13552}(507, \cdot)\) n/a 84320 40
13552.2.ge \(\chi_{13552}(289, \cdot)\) n/a 42080 80
13552.2.gf \(\chi_{13552}(211, \cdot)\) n/a 126720 80
13552.2.gg \(\chi_{13552}(531, \cdot)\) n/a 168640 80
13552.2.gl \(\chi_{13552}(13, \cdot)\) n/a 168640 80
13552.2.gm \(\chi_{13552}(141, \cdot)\) n/a 126720 80
13552.2.go \(\chi_{13552}(79, \cdot)\) n/a 42240 80
13552.2.gt \(\chi_{13552}(17, \cdot)\) n/a 42080 80
13552.2.gz \(\chi_{13552}(31, \cdot)\) n/a 42240 80
13552.2.he \(\chi_{13552}(59, \cdot)\) n/a 337280 160
13552.2.hf \(\chi_{13552}(51, \cdot)\) n/a 337280 160
13552.2.hg \(\chi_{13552}(37, \cdot)\) n/a 337280 160
13552.2.hh \(\chi_{13552}(61, \cdot)\) n/a 337280 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(13552))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(13552)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1694))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3388))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6776))\)\(^{\oplus 2}\)