↑

Properties

Label 8664.2
Level 8664
Weight 2
Dimension 870503
Nonzero newspaces 36
Sturm bound 8317440

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 8664 = 2^{3} \cdot 3 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(8317440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8664))\).

Total New Old
Modular forms 2091456 874251 1217205
Cusp forms 2067265 870503 1196762
Eisenstein series 24191 3748 20443

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8664))\)

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
8664.2.a \(\chi_{8664}(1, \cdot)\) 8664.2.a.a 1 1
8664.2.a.b 1
8664.2.a.c 1
8664.2.a.d 1
8664.2.a.e 1
8664.2.a.f 1
8664.2.a.g 1
8664.2.a.h 1
8664.2.a.i 1
8664.2.a.j 1
8664.2.a.k 1
8664.2.a.l 1
8664.2.a.m 1
8664.2.a.n 1
8664.2.a.o 1
8664.2.a.p 2
8664.2.a.q 2
8664.2.a.r 2
8664.2.a.s 2
8664.2.a.t 2
8664.2.a.u 2
8664.2.a.v 2
8664.2.a.w 2
8664.2.a.x 3
8664.2.a.y 3
8664.2.a.z 3
8664.2.a.ba 3
8664.2.a.bb 4
8664.2.a.bc 4
8664.2.a.bd 4
8664.2.a.be 4
8664.2.a.bf 6
8664.2.a.bg 6
8664.2.a.bh 6
8664.2.a.bi 6
8664.2.a.bj 6
8664.2.a.bk 6
8664.2.a.bl 8
8664.2.a.bm 8
8664.2.a.bn 9
8664.2.a.bo 9
8664.2.a.bp 9
8664.2.a.bq 9
8664.2.a.br 12
8664.2.a.bs 12
8664.2.d \(\chi_{8664}(7943, \cdot)\) None 0 1
8664.2.e \(\chi_{8664}(7219, \cdot)\) n/a 680 1
8664.2.f \(\chi_{8664}(6497, \cdot)\) n/a 340 1
8664.2.g \(\chi_{8664}(4333, \cdot)\) n/a 682 1
8664.2.j \(\chi_{8664}(3611, \cdot)\) n/a 1330 1
8664.2.k \(\chi_{8664}(2887, \cdot)\) None 0 1
8664.2.p \(\chi_{8664}(2165, \cdot)\) n/a 1328 1
8664.2.q \(\chi_{8664}(1873, \cdot)\) n/a 340 2
8664.2.t \(\chi_{8664}(1015, \cdot)\) None 0 2
8664.2.u \(\chi_{8664}(2819, \cdot)\) n/a 2656 2
8664.2.v \(\chi_{8664}(293, \cdot)\) n/a 2656 2
8664.2.y \(\chi_{8664}(5347, \cdot)\) n/a 1360 2
8664.2.z \(\chi_{8664}(1151, \cdot)\) None 0 2
8664.2.be \(\chi_{8664}(3541, \cdot)\) n/a 1360 2
8664.2.bf \(\chi_{8664}(4625, \cdot)\) n/a 680 2
8664.2.bg \(\chi_{8664}(2761, \cdot)\) n/a 1020 6
8664.2.bj \(\chi_{8664}(2789, \cdot)\) n/a 7968 6
8664.2.bk \(\chi_{8664}(2581, \cdot)\) n/a 4080 6
8664.2.bm \(\chi_{8664}(2465, \cdot)\) n/a 2040 6
8664.2.bp \(\chi_{8664}(307, \cdot)\) n/a 4080 6
8664.2.br \(\chi_{8664}(2039, \cdot)\) None 0 6
8664.2.bs \(\chi_{8664}(127, \cdot)\) None 0 6
8664.2.bu \(\chi_{8664}(1859, \cdot)\) n/a 7968 6
8664.2.bw \(\chi_{8664}(457, \cdot)\) n/a 3420 18
8664.2.bx \(\chi_{8664}(341, \cdot)\) n/a 27288 18
8664.2.cc \(\chi_{8664}(151, \cdot)\) None 0 18
8664.2.cd \(\chi_{8664}(419, \cdot)\) n/a 27288 18
8664.2.cg \(\chi_{8664}(229, \cdot)\) n/a 13680 18
8664.2.ch \(\chi_{8664}(113, \cdot)\) n/a 6840 18
8664.2.ci \(\chi_{8664}(379, \cdot)\) n/a 13680 18
8664.2.cj \(\chi_{8664}(191, \cdot)\) None 0 18
8664.2.cm \(\chi_{8664}(49, \cdot)\) n/a 6840 36
8664.2.cn \(\chi_{8664}(65, \cdot)\) n/a 13680 36
8664.2.co \(\chi_{8664}(277, \cdot)\) n/a 27360 36
8664.2.ct \(\chi_{8664}(239, \cdot)\) None 0 36
8664.2.cu \(\chi_{8664}(259, \cdot)\) n/a 27360 36
8664.2.cx \(\chi_{8664}(221, \cdot)\) n/a 54576 36
8664.2.cy \(\chi_{8664}(11, \cdot)\) n/a 54576 36
8664.2.cz \(\chi_{8664}(31, \cdot)\) None 0 36
8664.2.dc \(\chi_{8664}(25, \cdot)\) n/a 20520 108
8664.2.de \(\chi_{8664}(35, \cdot)\) n/a 163728 108
8664.2.dg \(\chi_{8664}(79, \cdot)\) None 0 108
8664.2.dh \(\chi_{8664}(23, \cdot)\) None 0 108
8664.2.dj \(\chi_{8664}(67, \cdot)\) n/a 82080 108
8664.2.dm \(\chi_{8664}(41, \cdot)\) n/a 41040 108
8664.2.do \(\chi_{8664}(61, \cdot)\) n/a 82080 108
8664.2.dp \(\chi_{8664}(29, \cdot)\) n/a 163728 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8664)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2166))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2888))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4332))\)\(^{\oplus 2}\)