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Properties

Label 5616.2
Level 5616
Weight 2
Dimension 380880
Nonzero newspaces 112
Sturm bound 3483648

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Defining parameters

Level: \( N \) = \( 5616 = 2^{4} \cdot 3^{3} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 112 \)
Sturm bound: \(3483648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5616))\).

Total New Old
Modular forms 880992 384048 496944
Cusp forms 860833 380880 479953
Eisenstein series 20159 3168 16991

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5616))\)

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
5616.2.a \(\chi_{5616}(1, \cdot)\) 5616.2.a.a 1 1
5616.2.a.b 1
5616.2.a.c 1
5616.2.a.d 1
5616.2.a.e 1
5616.2.a.f 1
5616.2.a.g 1
5616.2.a.h 1
5616.2.a.i 1
5616.2.a.j 1
5616.2.a.k 1
5616.2.a.l 1
5616.2.a.m 1
5616.2.a.n 1
5616.2.a.o 1
5616.2.a.p 1
5616.2.a.q 1
5616.2.a.r 1
5616.2.a.s 1
5616.2.a.t 1
5616.2.a.u 1
5616.2.a.v 1
5616.2.a.w 1
5616.2.a.x 1
5616.2.a.y 1
5616.2.a.z 1
5616.2.a.ba 1
5616.2.a.bb 1
5616.2.a.bc 1
5616.2.a.bd 1
5616.2.a.be 1
5616.2.a.bf 1
5616.2.a.bg 1
5616.2.a.bh 1
5616.2.a.bi 2
5616.2.a.bj 2
5616.2.a.bk 2
5616.2.a.bl 2
5616.2.a.bm 2
5616.2.a.bn 2
5616.2.a.bo 2
5616.2.a.bp 2
5616.2.a.bq 2
5616.2.a.br 2
5616.2.a.bs 2
5616.2.a.bt 2
5616.2.a.bu 2
5616.2.a.bv 2
5616.2.a.bw 2
5616.2.a.bx 2
5616.2.a.by 2
5616.2.a.bz 2
5616.2.a.ca 3
5616.2.a.cb 3
5616.2.a.cc 3
5616.2.a.cd 3
5616.2.a.ce 3
5616.2.a.cf 3
5616.2.a.cg 4
5616.2.a.ch 4
5616.2.c \(\chi_{5616}(3457, \cdot)\) n/a 112 1
5616.2.d \(\chi_{5616}(2159, \cdot)\) 5616.2.d.a 2 1
5616.2.d.b 2
5616.2.d.c 2
5616.2.d.d 2
5616.2.d.e 4
5616.2.d.f 4
5616.2.d.g 4
5616.2.d.h 4
5616.2.d.i 4
5616.2.d.j 4
5616.2.d.k 8
5616.2.d.l 8
5616.2.d.m 8
5616.2.d.n 8
5616.2.d.o 8
5616.2.d.p 8
5616.2.d.q 16
5616.2.g \(\chi_{5616}(2809, \cdot)\) None 0 1
5616.2.h \(\chi_{5616}(2807, \cdot)\) None 0 1
5616.2.j \(\chi_{5616}(4967, \cdot)\) None 0 1
5616.2.m \(\chi_{5616}(649, \cdot)\) None 0 1
5616.2.n \(\chi_{5616}(5615, \cdot)\) n/a 112 1
5616.2.q \(\chi_{5616}(1873, \cdot)\) n/a 144 2
5616.2.r \(\chi_{5616}(289, \cdot)\) n/a 164 2
5616.2.s \(\chi_{5616}(1153, \cdot)\) n/a 164 2
5616.2.t \(\chi_{5616}(2161, \cdot)\) n/a 224 2
5616.2.u \(\chi_{5616}(1243, \cdot)\) n/a 896 2
5616.2.x \(\chi_{5616}(1997, \cdot)\) n/a 896 2
5616.2.y \(\chi_{5616}(1403, \cdot)\) n/a 896 2
5616.2.ba \(\chi_{5616}(1405, \cdot)\) n/a 768 2
5616.2.be \(\chi_{5616}(2215, \cdot)\) None 0 2
5616.2.bf \(\chi_{5616}(5023, \cdot)\) n/a 224 2
5616.2.bi \(\chi_{5616}(161, \cdot)\) n/a 224 2
5616.2.bj \(\chi_{5616}(2969, \cdot)\) None 0 2
5616.2.bk \(\chi_{5616}(755, \cdot)\) n/a 768 2
5616.2.bm \(\chi_{5616}(2053, \cdot)\) n/a 896 2
5616.2.bp \(\chi_{5616}(1565, \cdot)\) n/a 896 2
5616.2.bq \(\chi_{5616}(811, \cdot)\) n/a 896 2
5616.2.bt \(\chi_{5616}(647, \cdot)\) None 0 2
5616.2.bu \(\chi_{5616}(217, \cdot)\) None 0 2
5616.2.bx \(\chi_{5616}(4319, \cdot)\) n/a 224 2
5616.2.by \(\chi_{5616}(433, \cdot)\) n/a 224 2
5616.2.ca \(\chi_{5616}(361, \cdot)\) None 0 2
5616.2.cd \(\chi_{5616}(4247, \cdot)\) None 0 2
5616.2.cf \(\chi_{5616}(719, \cdot)\) n/a 168 2
5616.2.ch \(\chi_{5616}(1871, \cdot)\) n/a 168 2
5616.2.cl \(\chi_{5616}(503, \cdot)\) None 0 2
5616.2.cn \(\chi_{5616}(2521, \cdot)\) None 0 2
5616.2.co \(\chi_{5616}(1223, \cdot)\) None 0 2
5616.2.cq \(\chi_{5616}(2233, \cdot)\) None 0 2
5616.2.cu \(\chi_{5616}(1583, \cdot)\) n/a 168 2
5616.2.cw \(\chi_{5616}(1439, \cdot)\) n/a 168 2
5616.2.cx \(\chi_{5616}(3169, \cdot)\) n/a 164 2
5616.2.cz \(\chi_{5616}(2089, \cdot)\) None 0 2
5616.2.db \(\chi_{5616}(935, \cdot)\) None 0 2
5616.2.de \(\chi_{5616}(937, \cdot)\) None 0 2
5616.2.dg \(\chi_{5616}(2519, \cdot)\) None 0 2
5616.2.dh \(\chi_{5616}(2305, \cdot)\) n/a 164 2
5616.2.dj \(\chi_{5616}(287, \cdot)\) n/a 144 2
5616.2.dm \(\chi_{5616}(1585, \cdot)\) n/a 164 2
5616.2.do \(\chi_{5616}(575, \cdot)\) n/a 168 2
5616.2.dq \(\chi_{5616}(1655, \cdot)\) None 0 2
5616.2.dr \(\chi_{5616}(1225, \cdot)\) None 0 2
5616.2.dv \(\chi_{5616}(2591, \cdot)\) n/a 224 2
5616.2.dw \(\chi_{5616}(3241, \cdot)\) None 0 2
5616.2.dz \(\chi_{5616}(1511, \cdot)\) None 0 2
5616.2.ea \(\chi_{5616}(625, \cdot)\) n/a 1296 6
5616.2.eb \(\chi_{5616}(529, \cdot)\) n/a 1500 6
5616.2.ec \(\chi_{5616}(1537, \cdot)\) n/a 1500 6
5616.2.ed \(\chi_{5616}(2429, \cdot)\) n/a 1792 4
5616.2.eg \(\chi_{5616}(1675, \cdot)\) n/a 1792 4
5616.2.eh \(\chi_{5616}(1493, \cdot)\) n/a 1328 4
5616.2.ej \(\chi_{5616}(307, \cdot)\) n/a 1328 4
5616.2.el \(\chi_{5616}(739, \cdot)\) n/a 1328 4
5616.2.eo \(\chi_{5616}(1709, \cdot)\) n/a 1328 4
5616.2.eq \(\chi_{5616}(1061, \cdot)\) n/a 1328 4
5616.2.es \(\chi_{5616}(955, \cdot)\) n/a 1328 4
5616.2.et \(\chi_{5616}(2557, \cdot)\) n/a 1328 4
5616.2.ev \(\chi_{5616}(179, \cdot)\) n/a 1328 4
5616.2.ey \(\chi_{5616}(1691, \cdot)\) n/a 1152 4
5616.2.fb \(\chi_{5616}(1837, \cdot)\) n/a 1792 4
5616.2.fc \(\chi_{5616}(829, \cdot)\) n/a 1328 4
5616.2.ff \(\chi_{5616}(107, \cdot)\) n/a 1792 4
5616.2.fg \(\chi_{5616}(1907, \cdot)\) n/a 1328 4
5616.2.fi \(\chi_{5616}(181, \cdot)\) n/a 1328 4
5616.2.fj \(\chi_{5616}(1279, \cdot)\) n/a 336 4
5616.2.fk \(\chi_{5616}(343, \cdot)\) None 0 4
5616.2.fp \(\chi_{5616}(1241, \cdot)\) None 0 4
5616.2.fq \(\chi_{5616}(1025, \cdot)\) n/a 448 4
5616.2.fr \(\chi_{5616}(449, \cdot)\) n/a 328 4
5616.2.fs \(\chi_{5616}(89, \cdot)\) None 0 4
5616.2.fx \(\chi_{5616}(665, \cdot)\) None 0 4
5616.2.fy \(\chi_{5616}(305, \cdot)\) n/a 328 4
5616.2.gb \(\chi_{5616}(271, \cdot)\) n/a 448 4
5616.2.gc \(\chi_{5616}(487, \cdot)\) None 0 4
5616.2.gd \(\chi_{5616}(631, \cdot)\) None 0 4
5616.2.ge \(\chi_{5616}(2719, \cdot)\) n/a 336 4
5616.2.gj \(\chi_{5616}(847, \cdot)\) n/a 336 4
5616.2.gk \(\chi_{5616}(2503, \cdot)\) None 0 4
5616.2.gl \(\chi_{5616}(1097, \cdot)\) None 0 4
5616.2.gm \(\chi_{5616}(2033, \cdot)\) n/a 328 4
5616.2.gq \(\chi_{5616}(467, \cdot)\) n/a 1328 4
5616.2.gt \(\chi_{5616}(757, \cdot)\) n/a 1792 4
5616.2.gu \(\chi_{5616}(685, \cdot)\) n/a 1328 4
5616.2.gx \(\chi_{5616}(1187, \cdot)\) n/a 1792 4
5616.2.gy \(\chi_{5616}(1115, \cdot)\) n/a 1328 4
5616.2.ha \(\chi_{5616}(469, \cdot)\) n/a 1152 4
5616.2.hb \(\chi_{5616}(1765, \cdot)\) n/a 1328 4
5616.2.hd \(\chi_{5616}(35, \cdot)\) n/a 1328 4
5616.2.hg \(\chi_{5616}(1315, \cdot)\) n/a 1328 4
5616.2.hi \(\chi_{5616}(557, \cdot)\) n/a 1328 4
5616.2.hk \(\chi_{5616}(125, \cdot)\) n/a 1328 4
5616.2.hl \(\chi_{5616}(1747, \cdot)\) n/a 1328 4
5616.2.hn \(\chi_{5616}(19, \cdot)\) n/a 1328 4
5616.2.hp \(\chi_{5616}(197, \cdot)\) n/a 1328 4
5616.2.hs \(\chi_{5616}(163, \cdot)\) n/a 1792 4
5616.2.ht \(\chi_{5616}(917, \cdot)\) n/a 1792 4
5616.2.hw \(\chi_{5616}(95, \cdot)\) n/a 1512 6
5616.2.hy \(\chi_{5616}(263, \cdot)\) None 0 6
5616.2.hz \(\chi_{5616}(815, \cdot)\) n/a 1512 6
5616.2.ib \(\chi_{5616}(1031, \cdot)\) None 0 6
5616.2.id \(\chi_{5616}(1465, \cdot)\) None 0 6
5616.2.if \(\chi_{5616}(49, \cdot)\) n/a 1500 6
5616.2.ii \(\chi_{5616}(25, \cdot)\) None 0 6
5616.2.il \(\chi_{5616}(337, \cdot)\) n/a 1500 6
5616.2.in \(\chi_{5616}(313, \cdot)\) None 0 6
5616.2.ip \(\chi_{5616}(745, \cdot)\) None 0 6
5616.2.is \(\chi_{5616}(23, \cdot)\) None 0 6
5616.2.iu \(\chi_{5616}(191, \cdot)\) n/a 1512 6
5616.2.iw \(\chi_{5616}(623, \cdot)\) n/a 1512 6
5616.2.iy \(\chi_{5616}(599, \cdot)\) None 0 6
5616.2.iz \(\chi_{5616}(911, \cdot)\) n/a 1296 6
5616.2.jb \(\chi_{5616}(311, \cdot)\) None 0 6
5616.2.jd \(\chi_{5616}(887, \cdot)\) None 0 6
5616.2.jf \(\chi_{5616}(959, \cdot)\) n/a 1512 6
5616.2.ji \(\chi_{5616}(121, \cdot)\) None 0 6
5616.2.jl \(\chi_{5616}(673, \cdot)\) n/a 1500 6
5616.2.jn \(\chi_{5616}(601, \cdot)\) None 0 6
5616.2.jp \(\chi_{5616}(115, \cdot)\) n/a 12048 12
5616.2.jq \(\chi_{5616}(583, \cdot)\) None 0 12
5616.2.js \(\chi_{5616}(347, \cdot)\) n/a 12048 12
5616.2.jt \(\chi_{5616}(563, \cdot)\) n/a 12048 12
5616.2.jx \(\chi_{5616}(175, \cdot)\) n/a 3024 12
5616.2.jy \(\chi_{5616}(643, \cdot)\) n/a 12048 12
5616.2.ka \(\chi_{5616}(605, \cdot)\) n/a 12048 12
5616.2.kc \(\chi_{5616}(317, \cdot)\) n/a 12048 12
5616.2.ke \(\chi_{5616}(401, \cdot)\) n/a 3000 12
5616.2.kh \(\chi_{5616}(281, \cdot)\) None 0 12
5616.2.ki \(\chi_{5616}(493, \cdot)\) n/a 12048 12
5616.2.kj \(\chi_{5616}(157, \cdot)\) n/a 10368 12
5616.2.km \(\chi_{5616}(277, \cdot)\) n/a 12048 12
5616.2.kn \(\chi_{5616}(61, \cdot)\) n/a 12048 12
5616.2.kq \(\chi_{5616}(785, \cdot)\) n/a 3000 12
5616.2.kt \(\chi_{5616}(41, \cdot)\) None 0 12
5616.2.kv \(\chi_{5616}(5, \cdot)\) n/a 12048 12
5616.2.kx \(\chi_{5616}(461, \cdot)\) n/a 12048 12
5616.2.kz \(\chi_{5616}(67, \cdot)\) n/a 12048 12
5616.2.lb \(\chi_{5616}(187, \cdot)\) n/a 12048 12
5616.2.ld \(\chi_{5616}(799, \cdot)\) n/a 3024 12
5616.2.le \(\chi_{5616}(151, \cdot)\) None 0 12
5616.2.li \(\chi_{5616}(491, \cdot)\) n/a 12048 12
5616.2.lj \(\chi_{5616}(419, \cdot)\) n/a 12048 12
5616.2.lm \(\chi_{5616}(155, \cdot)\) n/a 12048 12
5616.2.ln \(\chi_{5616}(131, \cdot)\) n/a 10368 12
5616.2.lp \(\chi_{5616}(31, \cdot)\) n/a 3024 12
5616.2.lq \(\chi_{5616}(7, \cdot)\) None 0 12
5616.2.ls \(\chi_{5616}(499, \cdot)\) n/a 12048 12
5616.2.lu \(\chi_{5616}(331, \cdot)\) n/a 12048 12
5616.2.lw \(\chi_{5616}(245, \cdot)\) n/a 12048 12
5616.2.lz \(\chi_{5616}(617, \cdot)\) None 0 12
5616.2.mc \(\chi_{5616}(133, \cdot)\) n/a 12048 12
5616.2.md \(\chi_{5616}(205, \cdot)\) n/a 12048 12
5616.2.me \(\chi_{5616}(353, \cdot)\) n/a 3000 12
5616.2.mh \(\chi_{5616}(149, \cdot)\) n/a 12048 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5616))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5616)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(702))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(936))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1404))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1872))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2808))\)\(^{\oplus 2}\)