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Properties

Label 8732.2
Level 8732
Weight 2
Dimension 1381704
Nonzero newspaces 36
Sturm bound 9521280

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Defining parameters

Level: \( N \) = \( 8732 = 2^{2} \cdot 37 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(9521280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8732))\).

Total New Old
Modular forms 2390760 1389680 1001080
Cusp forms 2369881 1381704 988177
Eisenstein series 20879 7976 12903

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8732))\)

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
8732.2.a \(\chi_{8732}(1, \cdot)\) 8732.2.a.a 1 1
8732.2.a.b 1
8732.2.a.c 41
8732.2.a.d 42
8732.2.a.e 44
8732.2.a.f 45
8732.2.c \(\chi_{8732}(8731, \cdot)\) n/a 1136 1
8732.2.e \(\chi_{8732}(3775, \cdot)\) n/a 1080 1
8732.2.g \(\chi_{8732}(4957, \cdot)\) n/a 186 1
8732.2.i \(\chi_{8732}(3541, \cdot)\) n/a 368 2
8732.2.k \(\chi_{8732}(117, \cdot)\) n/a 380 2
8732.2.m \(\chi_{8732}(5075, \cdot)\) n/a 2204 2
8732.2.p \(\chi_{8732}(1417, \cdot)\) n/a 372 2
8732.2.r \(\chi_{8732}(3303, \cdot)\) n/a 2272 2
8732.2.t \(\chi_{8732}(471, \cdot)\) n/a 2272 2
8732.2.u \(\chi_{8732}(1181, \cdot)\) n/a 1092 6
8732.2.w \(\chi_{8732}(119, \cdot)\) n/a 4408 4
8732.2.y \(\chi_{8732}(3893, \cdot)\) n/a 760 4
8732.2.z \(\chi_{8732}(1415, \cdot)\) n/a 6816 6
8732.2.ba \(\chi_{8732}(1653, \cdot)\) n/a 1104 6
8732.2.bb \(\chi_{8732}(707, \cdot)\) n/a 6816 6
8732.2.bg \(\chi_{8732}(593, \cdot)\) n/a 5040 28
8732.2.bh \(\chi_{8732}(355, \cdot)\) n/a 13224 12
8732.2.bi \(\chi_{8732}(353, \cdot)\) n/a 2280 12
8732.2.bm \(\chi_{8732}(369, \cdot)\) n/a 5320 28
8732.2.bo \(\chi_{8732}(519, \cdot)\) n/a 30240 28
8732.2.bq \(\chi_{8732}(443, \cdot)\) n/a 31808 28
8732.2.bs \(\chi_{8732}(121, \cdot)\) n/a 10640 56
8732.2.bt \(\chi_{8732}(475, \cdot)\) n/a 63616 56
8732.2.bv \(\chi_{8732}(401, \cdot)\) n/a 10640 56
8732.2.bx \(\chi_{8732}(11, \cdot)\) n/a 63616 56
8732.2.bz \(\chi_{8732}(47, \cdot)\) n/a 63616 56
8732.2.cb \(\chi_{8732}(85, \cdot)\) n/a 10640 56
8732.2.ce \(\chi_{8732}(9, \cdot)\) n/a 31920 168
8732.2.cf \(\chi_{8732}(97, \cdot)\) n/a 21280 112
8732.2.ch \(\chi_{8732}(51, \cdot)\) n/a 127232 112
8732.2.cn \(\chi_{8732}(67, \cdot)\) n/a 190848 168
8732.2.co \(\chi_{8732}(21, \cdot)\) n/a 31920 168
8732.2.cp \(\chi_{8732}(83, \cdot)\) n/a 190848 168
8732.2.cs \(\chi_{8732}(13, \cdot)\) n/a 63840 336
8732.2.ct \(\chi_{8732}(15, \cdot)\) n/a 381696 336

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8732))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8732)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2183))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4366))\)\(^{\oplus 2}\)