↑

Properties

Label 4928.2
Level 4928
Weight 2
Dimension 388836
Nonzero newspaces 64
Sturm bound 2949120

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 4928 = 2^{6} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(2949120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4928))\).

Total New Old
Modular forms 745920 392796 353124
Cusp forms 728641 388836 339805
Eisenstein series 17279 3960 13319

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4928))\)

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
4928.2.a \(\chi_{4928}(1, \cdot)\) 4928.2.a.a 1 1
4928.2.a.b 1
4928.2.a.c 1
4928.2.a.d 1
4928.2.a.e 1
4928.2.a.f 1
4928.2.a.g 1
4928.2.a.h 1
4928.2.a.i 1
4928.2.a.j 1
4928.2.a.k 1
4928.2.a.l 1
4928.2.a.m 1
4928.2.a.n 1
4928.2.a.o 1
4928.2.a.p 1
4928.2.a.q 1
4928.2.a.r 1
4928.2.a.s 1
4928.2.a.t 1
4928.2.a.u 1
4928.2.a.v 1
4928.2.a.w 1
4928.2.a.x 1
4928.2.a.y 1
4928.2.a.z 1
4928.2.a.ba 1
4928.2.a.bb 1
4928.2.a.bc 1
4928.2.a.bd 1
4928.2.a.be 1
4928.2.a.bf 1
4928.2.a.bg 1
4928.2.a.bh 1
4928.2.a.bi 1
4928.2.a.bj 1
4928.2.a.bk 2
4928.2.a.bl 2
4928.2.a.bm 2
4928.2.a.bn 2
4928.2.a.bo 2
4928.2.a.bp 2
4928.2.a.bq 2
4928.2.a.br 2
4928.2.a.bs 2
4928.2.a.bt 2
4928.2.a.bu 2
4928.2.a.bv 2
4928.2.a.bw 3
4928.2.a.bx 3
4928.2.a.by 3
4928.2.a.bz 3
4928.2.a.ca 3
4928.2.a.cb 3
4928.2.a.cc 4
4928.2.a.cd 4
4928.2.a.ce 4
4928.2.a.cf 4
4928.2.a.cg 4
4928.2.a.ch 4
4928.2.a.ci 4
4928.2.a.cj 4
4928.2.a.ck 5
4928.2.a.cl 5
4928.2.c \(\chi_{4928}(2465, \cdot)\) n/a 120 1
4928.2.e \(\chi_{4928}(769, \cdot)\) n/a 188 1
4928.2.f \(\chi_{4928}(2815, \cdot)\) n/a 144 1
4928.2.h \(\chi_{4928}(3807, \cdot)\) n/a 160 1
4928.2.j \(\chi_{4928}(1343, \cdot)\) n/a 160 1
4928.2.l \(\chi_{4928}(351, \cdot)\) n/a 144 1
4928.2.o \(\chi_{4928}(3233, \cdot)\) n/a 192 1
4928.2.q \(\chi_{4928}(1409, \cdot)\) n/a 320 2
4928.2.r \(\chi_{4928}(1583, \cdot)\) n/a 288 2
4928.2.s \(\chi_{4928}(111, \cdot)\) n/a 320 2
4928.2.x \(\chi_{4928}(2001, \cdot)\) n/a 376 2
4928.2.y \(\chi_{4928}(1233, \cdot)\) n/a 240 2
4928.2.z \(\chi_{4928}(449, \cdot)\) n/a 576 4
4928.2.ba \(\chi_{4928}(1825, \cdot)\) n/a 384 2
4928.2.be \(\chi_{4928}(2047, \cdot)\) n/a 320 2
4928.2.bg \(\chi_{4928}(1759, \cdot)\) n/a 384 2
4928.2.bi \(\chi_{4928}(2111, \cdot)\) n/a 376 2
4928.2.bk \(\chi_{4928}(2399, \cdot)\) n/a 320 2
4928.2.bl \(\chi_{4928}(1761, \cdot)\) n/a 320 2
4928.2.bn \(\chi_{4928}(1473, \cdot)\) n/a 376 2
4928.2.bp \(\chi_{4928}(153, \cdot)\) None 0 4
4928.2.bq \(\chi_{4928}(617, \cdot)\) None 0 4
4928.2.bv \(\chi_{4928}(967, \cdot)\) None 0 4
4928.2.bw \(\chi_{4928}(727, \cdot)\) None 0 4
4928.2.by \(\chi_{4928}(545, \cdot)\) n/a 768 4
4928.2.cb \(\chi_{4928}(799, \cdot)\) n/a 576 4
4928.2.cd \(\chi_{4928}(895, \cdot)\) n/a 752 4
4928.2.cf \(\chi_{4928}(223, \cdot)\) n/a 768 4
4928.2.ch \(\chi_{4928}(127, \cdot)\) n/a 576 4
4928.2.ci \(\chi_{4928}(321, \cdot)\) n/a 752 4
4928.2.ck \(\chi_{4928}(225, \cdot)\) n/a 576 4
4928.2.co \(\chi_{4928}(815, \cdot)\) n/a 640 4
4928.2.cp \(\chi_{4928}(527, \cdot)\) n/a 752 4
4928.2.cq \(\chi_{4928}(177, \cdot)\) n/a 640 4
4928.2.cr \(\chi_{4928}(241, \cdot)\) n/a 752 4
4928.2.cu \(\chi_{4928}(641, \cdot)\) n/a 1504 8
4928.2.cx \(\chi_{4928}(309, \cdot)\) n/a 3840 8
4928.2.cy \(\chi_{4928}(419, \cdot)\) n/a 5120 8
4928.2.cz \(\chi_{4928}(43, \cdot)\) n/a 4608 8
4928.2.da \(\chi_{4928}(461, \cdot)\) n/a 6112 8
4928.2.dd \(\chi_{4928}(113, \cdot)\) n/a 1152 8
4928.2.de \(\chi_{4928}(657, \cdot)\) n/a 1504 8
4928.2.dj \(\chi_{4928}(335, \cdot)\) n/a 1504 8
4928.2.dk \(\chi_{4928}(239, \cdot)\) n/a 1152 8
4928.2.dn \(\chi_{4928}(793, \cdot)\) None 0 8
4928.2.do \(\chi_{4928}(857, \cdot)\) None 0 8
4928.2.dp \(\chi_{4928}(199, \cdot)\) None 0 8
4928.2.dq \(\chi_{4928}(263, \cdot)\) None 0 8
4928.2.du \(\chi_{4928}(129, \cdot)\) n/a 1504 8
4928.2.dw \(\chi_{4928}(289, \cdot)\) n/a 1536 8
4928.2.dx \(\chi_{4928}(31, \cdot)\) n/a 1536 8
4928.2.dz \(\chi_{4928}(767, \cdot)\) n/a 1504 8
4928.2.eb \(\chi_{4928}(95, \cdot)\) n/a 1536 8
4928.2.ed \(\chi_{4928}(383, \cdot)\) n/a 1504 8
4928.2.eh \(\chi_{4928}(481, \cdot)\) n/a 1536 8
4928.2.ei \(\chi_{4928}(279, \cdot)\) None 0 16
4928.2.ej \(\chi_{4928}(183, \cdot)\) None 0 16
4928.2.eo \(\chi_{4928}(169, \cdot)\) None 0 16
4928.2.ep \(\chi_{4928}(41, \cdot)\) None 0 16
4928.2.es \(\chi_{4928}(285, \cdot)\) n/a 12224 16
4928.2.et \(\chi_{4928}(219, \cdot)\) n/a 12224 16
4928.2.eu \(\chi_{4928}(243, \cdot)\) n/a 10240 16
4928.2.ev \(\chi_{4928}(221, \cdot)\) n/a 10240 16
4928.2.fa \(\chi_{4928}(17, \cdot)\) n/a 3008 16
4928.2.fb \(\chi_{4928}(81, \cdot)\) n/a 3008 16
4928.2.fc \(\chi_{4928}(79, \cdot)\) n/a 3008 16
4928.2.fd \(\chi_{4928}(47, \cdot)\) n/a 3008 16
4928.2.fg \(\chi_{4928}(13, \cdot)\) n/a 24448 32
4928.2.fh \(\chi_{4928}(211, \cdot)\) n/a 18432 32
4928.2.fm \(\chi_{4928}(27, \cdot)\) n/a 24448 32
4928.2.fn \(\chi_{4928}(141, \cdot)\) n/a 18432 32
4928.2.fq \(\chi_{4928}(39, \cdot)\) None 0 32
4928.2.fr \(\chi_{4928}(103, \cdot)\) None 0 32
4928.2.fs \(\chi_{4928}(73, \cdot)\) None 0 32
4928.2.ft \(\chi_{4928}(9, \cdot)\) None 0 32
4928.2.fw \(\chi_{4928}(37, \cdot)\) n/a 48896 64
4928.2.fx \(\chi_{4928}(3, \cdot)\) n/a 48896 64
4928.2.gc \(\chi_{4928}(51, \cdot)\) n/a 48896 64
4928.2.gd \(\chi_{4928}(61, \cdot)\) n/a 48896 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4928))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4928)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1232))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2464))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4928))\)\(^{\oplus 1}\)