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Properties

Label 7248.2
Level 7248
Weight 2
Dimension 614204
Nonzero newspaces 48
Sturm bound 5836800

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Defining parameters

Level: \( N \) = \( 7248 = 2^{4} \cdot 3 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(5836800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7248))\).

Total New Old
Modular forms 1467600 616888 850712
Cusp forms 1450801 614204 836597
Eisenstein series 16799 2684 14115

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7248))\)

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
7248.2.a \(\chi_{7248}(1, \cdot)\) 7248.2.a.a 1 1
7248.2.a.b 1
7248.2.a.c 1
7248.2.a.d 1
7248.2.a.e 1
7248.2.a.f 1
7248.2.a.g 1
7248.2.a.h 1
7248.2.a.i 1
7248.2.a.j 1
7248.2.a.k 1
7248.2.a.l 1
7248.2.a.m 1
7248.2.a.n 2
7248.2.a.o 2
7248.2.a.p 2
7248.2.a.q 2
7248.2.a.r 2
7248.2.a.s 2
7248.2.a.t 2
7248.2.a.u 3
7248.2.a.v 3
7248.2.a.w 3
7248.2.a.x 3
7248.2.a.y 3
7248.2.a.z 4
7248.2.a.ba 4
7248.2.a.bb 4
7248.2.a.bc 4
7248.2.a.bd 4
7248.2.a.be 4
7248.2.a.bf 4
7248.2.a.bg 5
7248.2.a.bh 5
7248.2.a.bi 5
7248.2.a.bj 5
7248.2.a.bk 8
7248.2.a.bl 9
7248.2.a.bm 10
7248.2.a.bn 10
7248.2.a.bo 11
7248.2.a.bp 12
7248.2.b \(\chi_{7248}(4529, \cdot)\) n/a 302 1
7248.2.e \(\chi_{7248}(5135, \cdot)\) n/a 300 1
7248.2.f \(\chi_{7248}(3625, \cdot)\) None 0 1
7248.2.i \(\chi_{7248}(1207, \cdot)\) None 0 1
7248.2.j \(\chi_{7248}(1511, \cdot)\) None 0 1
7248.2.m \(\chi_{7248}(905, \cdot)\) None 0 1
7248.2.n \(\chi_{7248}(4831, \cdot)\) n/a 152 1
7248.2.q \(\chi_{7248}(3505, \cdot)\) n/a 304 2
7248.2.t \(\chi_{7248}(3019, \cdot)\) n/a 1216 2
7248.2.u \(\chi_{7248}(1813, \cdot)\) n/a 1200 2
7248.2.v \(\chi_{7248}(3323, \cdot)\) n/a 2400 2
7248.2.w \(\chi_{7248}(2717, \cdot)\) n/a 2424 2
7248.2.z \(\chi_{7248}(2737, \cdot)\) n/a 608 4
7248.2.bc \(\chi_{7248}(1327, \cdot)\) n/a 304 2
7248.2.bd \(\chi_{7248}(1241, \cdot)\) None 0 2
7248.2.bg \(\chi_{7248}(1175, \cdot)\) None 0 2
7248.2.bh \(\chi_{7248}(1543, \cdot)\) None 0 2
7248.2.bk \(\chi_{7248}(3289, \cdot)\) None 0 2
7248.2.bl \(\chi_{7248}(1391, \cdot)\) n/a 608 2
7248.2.bo \(\chi_{7248}(1025, \cdot)\) n/a 604 2
7248.2.br \(\chi_{7248}(847, \cdot)\) n/a 608 4
7248.2.bs \(\chi_{7248}(1049, \cdot)\) None 0 4
7248.2.bv \(\chi_{7248}(215, \cdot)\) None 0 4
7248.2.bw \(\chi_{7248}(1351, \cdot)\) None 0 4
7248.2.bz \(\chi_{7248}(361, \cdot)\) None 0 4
7248.2.ca \(\chi_{7248}(623, \cdot)\) n/a 1216 4
7248.2.cd \(\chi_{7248}(545, \cdot)\) n/a 1208 4
7248.2.cg \(\chi_{7248}(2837, \cdot)\) n/a 4848 4
7248.2.ch \(\chi_{7248}(2987, \cdot)\) n/a 4848 4
7248.2.ci \(\chi_{7248}(1477, \cdot)\) n/a 2432 4
7248.2.cj \(\chi_{7248}(3139, \cdot)\) n/a 2432 4
7248.2.cm \(\chi_{7248}(529, \cdot)\) n/a 1216 8
7248.2.cp \(\chi_{7248}(389, \cdot)\) n/a 9696 8
7248.2.cq \(\chi_{7248}(59, \cdot)\) n/a 9696 8
7248.2.cr \(\chi_{7248}(517, \cdot)\) n/a 4864 8
7248.2.cs \(\chi_{7248}(283, \cdot)\) n/a 4864 8
7248.2.cv \(\chi_{7248}(577, \cdot)\) n/a 3040 20
7248.2.cw \(\chi_{7248}(113, \cdot)\) n/a 2416 8
7248.2.cz \(\chi_{7248}(1487, \cdot)\) n/a 2432 8
7248.2.da \(\chi_{7248}(457, \cdot)\) None 0 8
7248.2.dd \(\chi_{7248}(679, \cdot)\) None 0 8
7248.2.de \(\chi_{7248}(167, \cdot)\) None 0 8
7248.2.dh \(\chi_{7248}(377, \cdot)\) None 0 8
7248.2.di \(\chi_{7248}(415, \cdot)\) n/a 1216 8
7248.2.dl \(\chi_{7248}(343, \cdot)\) None 0 20
7248.2.dm \(\chi_{7248}(65, \cdot)\) n/a 6040 20
7248.2.dn \(\chi_{7248}(311, \cdot)\) None 0 20
7248.2.ds \(\chi_{7248}(383, \cdot)\) n/a 6080 20
7248.2.dt \(\chi_{7248}(41, \cdot)\) None 0 20
7248.2.du \(\chi_{7248}(79, \cdot)\) n/a 3040 20
7248.2.dv \(\chi_{7248}(601, \cdot)\) None 0 20
7248.2.ec \(\chi_{7248}(451, \cdot)\) n/a 9728 16
7248.2.ed \(\chi_{7248}(85, \cdot)\) n/a 9728 16
7248.2.ee \(\chi_{7248}(155, \cdot)\) n/a 19392 16
7248.2.ef \(\chi_{7248}(149, \cdot)\) n/a 19392 16
7248.2.ei \(\chi_{7248}(49, \cdot)\) n/a 6080 40
7248.2.en \(\chi_{7248}(53, \cdot)\) n/a 48480 40
7248.2.eo \(\chi_{7248}(229, \cdot)\) n/a 24320 40
7248.2.ep \(\chi_{7248}(67, \cdot)\) n/a 24320 40
7248.2.eq \(\chi_{7248}(275, \cdot)\) n/a 48480 40
7248.2.ev \(\chi_{7248}(7, \cdot)\) None 0 40
7248.2.ew \(\chi_{7248}(647, \cdot)\) None 0 40
7248.2.ex \(\chi_{7248}(257, \cdot)\) n/a 12080 40
7248.2.fc \(\chi_{7248}(89, \cdot)\) None 0 40
7248.2.fd \(\chi_{7248}(47, \cdot)\) n/a 12160 40
7248.2.fe \(\chi_{7248}(25, \cdot)\) None 0 40
7248.2.ff \(\chi_{7248}(271, \cdot)\) n/a 6080 40
7248.2.fg \(\chi_{7248}(11, \cdot)\) n/a 96960 80
7248.2.fh \(\chi_{7248}(115, \cdot)\) n/a 48640 80
7248.2.fi \(\chi_{7248}(37, \cdot)\) n/a 48640 80
7248.2.fj \(\chi_{7248}(77, \cdot)\) n/a 96960 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7248))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7248)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(302))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(453))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(604))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(906))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1812))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7248))\)\(^{\oplus 1}\)