Properties

Label 8752.2
Level 8752
Weight 2
Dimension 1343975
Nonzero newspaces 32
Sturm bound 9574656

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Defining parameters

Level: \( N \) = \( 8752 = 2^{4} \cdot 547 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(9574656\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8752))\).

Total New Old
Modular forms 2401308 1348879 1052429
Cusp forms 2386021 1343975 1042046
Eisenstein series 15287 4904 10383

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8752))\)

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
8752.2.a \(\chi_{8752}(1, \cdot)\) 8752.2.a.a 1 1
8752.2.a.b 1
8752.2.a.c 1
8752.2.a.d 1
8752.2.a.e 1
8752.2.a.f 1
8752.2.a.g 1
8752.2.a.h 1
8752.2.a.i 1
8752.2.a.j 1
8752.2.a.k 1
8752.2.a.l 2
8752.2.a.m 2
8752.2.a.n 2
8752.2.a.o 7
8752.2.a.p 7
8752.2.a.q 13
8752.2.a.r 15
8752.2.a.s 18
8752.2.a.t 19
8752.2.a.u 23
8752.2.a.v 25
8752.2.a.w 27
8752.2.a.x 31
8752.2.a.y 34
8752.2.a.z 37
8752.2.c \(\chi_{8752}(4377, \cdot)\) None 0 1
8752.2.e \(\chi_{8752}(4375, \cdot)\) None 0 1
8752.2.g \(\chi_{8752}(8751, \cdot)\) n/a 274 1
8752.2.i \(\chi_{8752}(1681, \cdot)\) n/a 546 2
8752.2.j \(\chi_{8752}(2187, \cdot)\) n/a 2188 2
8752.2.k \(\chi_{8752}(2189, \cdot)\) n/a 2184 2
8752.2.n \(\chi_{8752}(2695, \cdot)\) None 0 2
8752.2.p \(\chi_{8752}(3241, \cdot)\) None 0 2
8752.2.s \(\chi_{8752}(1135, \cdot)\) n/a 548 2
8752.2.u \(\chi_{8752}(81, \cdot)\) n/a 1638 6
8752.2.x \(\chi_{8752}(1053, \cdot)\) n/a 4376 4
8752.2.y \(\chi_{8752}(507, \cdot)\) n/a 4376 4
8752.2.z \(\chi_{8752}(353, \cdot)\) n/a 3276 12
8752.2.bb \(\chi_{8752}(2191, \cdot)\) n/a 1644 6
8752.2.bd \(\chi_{8752}(2215, \cdot)\) None 0 6
8752.2.bf \(\chi_{8752}(9, \cdot)\) None 0 6
8752.2.bh \(\chi_{8752}(561, \cdot)\) n/a 3276 12
8752.2.bi \(\chi_{8752}(1671, \cdot)\) None 0 12
8752.2.bk \(\chi_{8752}(2425, \cdot)\) None 0 12
8752.2.bn \(\chi_{8752}(575, \cdot)\) n/a 3288 12
8752.2.br \(\chi_{8752}(2197, \cdot)\) n/a 13128 12
8752.2.bs \(\chi_{8752}(3, \cdot)\) n/a 13128 12
8752.2.bt \(\chi_{8752}(129, \cdot)\) n/a 6552 24
8752.2.bv \(\chi_{8752}(351, \cdot)\) n/a 3288 12
8752.2.by \(\chi_{8752}(169, \cdot)\) None 0 12
8752.2.ca \(\chi_{8752}(39, \cdot)\) None 0 12
8752.2.cd \(\chi_{8752}(237, \cdot)\) n/a 26256 24
8752.2.ce \(\chi_{8752}(107, \cdot)\) n/a 26256 24
8752.2.cg \(\chi_{8752}(121, \cdot)\) None 0 24
8752.2.ci \(\chi_{8752}(855, \cdot)\) None 0 24
8752.2.ck \(\chi_{8752}(863, \cdot)\) n/a 6576 24
8752.2.cm \(\chi_{8752}(187, \cdot)\) n/a 26256 24
8752.2.cn \(\chi_{8752}(13, \cdot)\) n/a 26256 24
8752.2.cq \(\chi_{8752}(161, \cdot)\) n/a 19656 72
8752.2.cr \(\chi_{8752}(59, \cdot)\) n/a 52512 48
8752.2.cs \(\chi_{8752}(21, \cdot)\) n/a 52512 48
8752.2.cw \(\chi_{8752}(31, \cdot)\) n/a 19728 72
8752.2.cz \(\chi_{8752}(185, \cdot)\) None 0 72
8752.2.db \(\chi_{8752}(55, \cdot)\) None 0 72
8752.2.dc \(\chi_{8752}(49, \cdot)\) n/a 39312 144
8752.2.dd \(\chi_{8752}(299, \cdot)\) n/a 157536 144
8752.2.de \(\chi_{8752}(29, \cdot)\) n/a 157536 144
8752.2.di \(\chi_{8752}(63, \cdot)\) n/a 39456 144
8752.2.dk \(\chi_{8752}(7, \cdot)\) None 0 144
8752.2.dm \(\chi_{8752}(25, \cdot)\) None 0 144
8752.2.dq \(\chi_{8752}(53, \cdot)\) n/a 315072 288
8752.2.dr \(\chi_{8752}(43, \cdot)\) n/a 315072 288

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8752))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8752)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(547))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1094))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2188))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4376))\)\(^{\oplus 2}\)