Properties

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

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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 the 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

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