# Properties

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

## 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 the 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

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