# Properties

 Label 7728.2 Level 7728 Weight 2 Dimension 651404 Nonzero newspaces 64 Sturm bound 6488064

## Defining parameters

 Level: $$N$$ = $$7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$6488064$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7728))$$.

Total New Old
Modular forms 1636800 655180 981620
Cusp forms 1607233 651404 955829
Eisenstein series 29567 3776 25791

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7728))$$

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
7728.2.a $$\chi_{7728}(1, \cdot)$$ 7728.2.a.a 1 1
7728.2.a.b 1
7728.2.a.c 1
7728.2.a.d 1
7728.2.a.e 1
7728.2.a.f 1
7728.2.a.g 1
7728.2.a.h 1
7728.2.a.i 1
7728.2.a.j 1
7728.2.a.k 1
7728.2.a.l 1
7728.2.a.m 1
7728.2.a.n 1
7728.2.a.o 1
7728.2.a.p 1
7728.2.a.q 1
7728.2.a.r 1
7728.2.a.s 1
7728.2.a.t 1
7728.2.a.u 1
7728.2.a.v 2
7728.2.a.w 2
7728.2.a.x 2
7728.2.a.y 2
7728.2.a.z 2
7728.2.a.ba 2
7728.2.a.bb 2
7728.2.a.bc 2
7728.2.a.bd 2
7728.2.a.be 2
7728.2.a.bf 2
7728.2.a.bg 2
7728.2.a.bh 2
7728.2.a.bi 2
7728.2.a.bj 2
7728.2.a.bk 2
7728.2.a.bl 2
7728.2.a.bm 2
7728.2.a.bn 2
7728.2.a.bo 2
7728.2.a.bp 3
7728.2.a.bq 3
7728.2.a.br 3
7728.2.a.bs 3
7728.2.a.bt 3
7728.2.a.bu 3
7728.2.a.bv 3
7728.2.a.bw 3
7728.2.a.bx 3
7728.2.a.by 3
7728.2.a.bz 4
7728.2.a.ca 4
7728.2.a.cb 4
7728.2.a.cc 4
7728.2.a.cd 4
7728.2.a.ce 4
7728.2.a.cf 5
7728.2.a.cg 6
7728.2.a.ch 6
7728.2.b $$\chi_{7728}(7727, \cdot)$$ n/a 384 1
7728.2.c $$\chi_{7728}(5935, \cdot)$$ n/a 176 1
7728.2.d $$\chi_{7728}(3865, \cdot)$$ None 0 1
7728.2.e $$\chi_{7728}(5657, \cdot)$$ None 0 1
7728.2.n $$\chi_{7728}(2255, \cdot)$$ n/a 264 1
7728.2.o $$\chi_{7728}(1471, \cdot)$$ n/a 144 1
7728.2.p $$\chi_{7728}(1609, \cdot)$$ None 0 1
7728.2.q $$\chi_{7728}(2393, \cdot)$$ None 0 1
7728.2.r $$\chi_{7728}(5335, \cdot)$$ None 0 1
7728.2.s $$\chi_{7728}(6119, \cdot)$$ None 0 1
7728.2.t $$\chi_{7728}(6257, \cdot)$$ n/a 352 1
7728.2.u $$\chi_{7728}(5473, \cdot)$$ n/a 192 1
7728.2.bd $$\chi_{7728}(2071, \cdot)$$ None 0 1
7728.2.be $$\chi_{7728}(3863, \cdot)$$ None 0 1
7728.2.bf $$\chi_{7728}(1793, \cdot)$$ n/a 288 1
7728.2.bg $$\chi_{7728}(2209, \cdot)$$ n/a 352 2
7728.2.bh $$\chi_{7728}(3403, \cdot)$$ n/a 1152 2
7728.2.bk $$\chi_{7728}(323, \cdot)$$ n/a 2112 2
7728.2.bl $$\chi_{7728}(1931, \cdot)$$ n/a 3056 2
7728.2.bo $$\chi_{7728}(139, \cdot)$$ n/a 1408 2
7728.2.bq $$\chi_{7728}(461, \cdot)$$ n/a 2816 2
7728.2.br $$\chi_{7728}(3541, \cdot)$$ n/a 1536 2
7728.2.bu $$\chi_{7728}(1933, \cdot)$$ n/a 1056 2
7728.2.bv $$\chi_{7728}(3725, \cdot)$$ n/a 2304 2
7728.2.cb $$\chi_{7728}(4001, \cdot)$$ n/a 760 2
7728.2.cc $$\chi_{7728}(551, \cdot)$$ None 0 2
7728.2.cd $$\chi_{7728}(6487, \cdot)$$ None 0 2
7728.2.ce $$\chi_{7728}(2161, \cdot)$$ n/a 384 2
7728.2.cf $$\chi_{7728}(2945, \cdot)$$ n/a 704 2
7728.2.cg $$\chi_{7728}(599, \cdot)$$ None 0 2
7728.2.ch $$\chi_{7728}(919, \cdot)$$ None 0 2
7728.2.cq $$\chi_{7728}(185, \cdot)$$ None 0 2
7728.2.cr $$\chi_{7728}(6025, \cdot)$$ None 0 2
7728.2.cs $$\chi_{7728}(3679, \cdot)$$ n/a 384 2
7728.2.ct $$\chi_{7728}(4463, \cdot)$$ n/a 704 2
7728.2.cu $$\chi_{7728}(137, \cdot)$$ None 0 2
7728.2.cv $$\chi_{7728}(6073, \cdot)$$ None 0 2
7728.2.cw $$\chi_{7728}(2623, \cdot)$$ n/a 352 2
7728.2.cx $$\chi_{7728}(4415, \cdot)$$ n/a 768 2
7728.2.dc $$\chi_{7728}(673, \cdot)$$ n/a 1440 10
7728.2.dd $$\chi_{7728}(277, \cdot)$$ n/a 2816 4
7728.2.dg $$\chi_{7728}(2069, \cdot)$$ n/a 6112 4
7728.2.dh $$\chi_{7728}(1013, \cdot)$$ n/a 5632 4
7728.2.dk $$\chi_{7728}(229, \cdot)$$ n/a 3072 4
7728.2.dm $$\chi_{7728}(2483, \cdot)$$ n/a 6112 4
7728.2.dn $$\chi_{7728}(691, \cdot)$$ n/a 2816 4
7728.2.dq $$\chi_{7728}(1747, \cdot)$$ n/a 3072 4
7728.2.dr $$\chi_{7728}(2531, \cdot)$$ n/a 5632 4
7728.2.dt $$\chi_{7728}(113, \cdot)$$ n/a 2880 10
7728.2.du $$\chi_{7728}(503, \cdot)$$ None 0 10
7728.2.dv $$\chi_{7728}(55, \cdot)$$ None 0 10
7728.2.ee $$\chi_{7728}(97, \cdot)$$ n/a 1920 10
7728.2.ef $$\chi_{7728}(209, \cdot)$$ n/a 3800 10
7728.2.eg $$\chi_{7728}(71, \cdot)$$ None 0 10
7728.2.eh $$\chi_{7728}(295, \cdot)$$ None 0 10
7728.2.ei $$\chi_{7728}(41, \cdot)$$ None 0 10
7728.2.ej $$\chi_{7728}(937, \cdot)$$ None 0 10
7728.2.ek $$\chi_{7728}(799, \cdot)$$ n/a 1440 10
7728.2.el $$\chi_{7728}(239, \cdot)$$ n/a 2880 10
7728.2.eu $$\chi_{7728}(281, \cdot)$$ None 0 10
7728.2.ev $$\chi_{7728}(169, \cdot)$$ None 0 10
7728.2.ew $$\chi_{7728}(223, \cdot)$$ n/a 1920 10
7728.2.ex $$\chi_{7728}(2015, \cdot)$$ n/a 3840 10
7728.2.ey $$\chi_{7728}(193, \cdot)$$ n/a 3840 20
7728.2.ez $$\chi_{7728}(365, \cdot)$$ n/a 23040 20
7728.2.fc $$\chi_{7728}(85, \cdot)$$ n/a 11520 20
7728.2.fd $$\chi_{7728}(181, \cdot)$$ n/a 15360 20
7728.2.fg $$\chi_{7728}(629, \cdot)$$ n/a 30560 20
7728.2.fi $$\chi_{7728}(307, \cdot)$$ n/a 15360 20
7728.2.fj $$\chi_{7728}(83, \cdot)$$ n/a 30560 20
7728.2.fm $$\chi_{7728}(491, \cdot)$$ n/a 23040 20
7728.2.fn $$\chi_{7728}(43, \cdot)$$ n/a 11520 20
7728.2.ft $$\chi_{7728}(143, \cdot)$$ n/a 7680 20
7728.2.fu $$\chi_{7728}(31, \cdot)$$ n/a 3840 20
7728.2.fv $$\chi_{7728}(25, \cdot)$$ None 0 20
7728.2.fw $$\chi_{7728}(569, \cdot)$$ None 0 20
7728.2.fx $$\chi_{7728}(95, \cdot)$$ n/a 7680 20
7728.2.fy $$\chi_{7728}(79, \cdot)$$ n/a 3840 20
7728.2.fz $$\chi_{7728}(313, \cdot)$$ None 0 20
7728.2.ga $$\chi_{7728}(761, \cdot)$$ None 0 20
7728.2.gj $$\chi_{7728}(247, \cdot)$$ None 0 20
7728.2.gk $$\chi_{7728}(1271, \cdot)$$ None 0 20
7728.2.gl $$\chi_{7728}(257, \cdot)$$ n/a 7600 20
7728.2.gm $$\chi_{7728}(145, \cdot)$$ n/a 3840 20
7728.2.gn $$\chi_{7728}(439, \cdot)$$ None 0 20
7728.2.go $$\chi_{7728}(983, \cdot)$$ None 0 20
7728.2.gp $$\chi_{7728}(65, \cdot)$$ n/a 7600 20
7728.2.gu $$\chi_{7728}(179, \cdot)$$ n/a 61120 40
7728.2.gx $$\chi_{7728}(67, \cdot)$$ n/a 30720 40
7728.2.gy $$\chi_{7728}(187, \cdot)$$ n/a 30720 40
7728.2.hb $$\chi_{7728}(227, \cdot)$$ n/a 61120 40
7728.2.hd $$\chi_{7728}(61, \cdot)$$ n/a 30720 40
7728.2.he $$\chi_{7728}(101, \cdot)$$ n/a 61120 40
7728.2.hh $$\chi_{7728}(53, \cdot)$$ n/a 61120 40
7728.2.hi $$\chi_{7728}(445, \cdot)$$ n/a 30720 40

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7728))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7728)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 40}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(276))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(322))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(368))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(483))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(552))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(644))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(966))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1104))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1288))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1932))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2576))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3864))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7728))$$$$^{\oplus 1}$$