↑

Properties

Label 9984.2
Level 9984
Weight 2
Dimension 1145104
Nonzero newspaces 88
Sturm bound 11010048

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 9984 = 2^{8} \cdot 3 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 88 \)
Sturm bound: \(11010048\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9984))\).

Total New Old
Modular forms 2769408 1149680 1619728
Cusp forms 2735617 1145104 1590513
Eisenstein series 33791 4576 29215

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9984))\)

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
9984.2.a \(\chi_{9984}(1, \cdot)\) 9984.2.a.a 2 1
9984.2.a.b 2
9984.2.a.c 2
9984.2.a.d 2
9984.2.a.e 2
9984.2.a.f 2
9984.2.a.g 2
9984.2.a.h 2
9984.2.a.i 2
9984.2.a.j 2
9984.2.a.k 2
9984.2.a.l 2
9984.2.a.m 2
9984.2.a.n 2
9984.2.a.o 2
9984.2.a.p 2
9984.2.a.q 4
9984.2.a.r 4
9984.2.a.s 4
9984.2.a.t 4
9984.2.a.u 4
9984.2.a.v 4
9984.2.a.w 4
9984.2.a.x 4
9984.2.a.y 4
9984.2.a.z 4
9984.2.a.ba 4
9984.2.a.bb 4
9984.2.a.bc 4
9984.2.a.bd 4
9984.2.a.be 4
9984.2.a.bf 4
9984.2.a.bg 4
9984.2.a.bh 4
9984.2.a.bi 4
9984.2.a.bj 4
9984.2.a.bk 6
9984.2.a.bl 6
9984.2.a.bm 6
9984.2.a.bn 6
9984.2.a.bo 6
9984.2.a.bp 6
9984.2.a.bq 6
9984.2.a.br 6
9984.2.a.bs 8
9984.2.a.bt 8
9984.2.a.bu 8
9984.2.a.bv 8
9984.2.c \(\chi_{9984}(8449, \cdot)\) n/a 224 1
9984.2.d \(\chi_{9984}(1535, \cdot)\) n/a 384 1
9984.2.g \(\chi_{9984}(4993, \cdot)\) n/a 192 1
9984.2.h \(\chi_{9984}(4991, \cdot)\) n/a 440 1
9984.2.j \(\chi_{9984}(6527, \cdot)\) n/a 384 1
9984.2.m \(\chi_{9984}(3457, \cdot)\) n/a 224 1
9984.2.n \(\chi_{9984}(9983, \cdot)\) n/a 440 1
9984.2.q \(\chi_{9984}(1537, \cdot)\) n/a 448 2
9984.2.r \(\chi_{9984}(1087, \cdot)\) n/a 448 2
9984.2.u \(\chi_{9984}(6209, \cdot)\) n/a 896 2
9984.2.v \(\chi_{9984}(2495, \cdot)\) n/a 896 2
9984.2.x \(\chi_{9984}(2497, \cdot)\) n/a 384 2
9984.2.bb \(\chi_{9984}(6271, \cdot)\) n/a 448 2
9984.2.bc \(\chi_{9984}(1279, \cdot)\) n/a 448 2
9984.2.bf \(\chi_{9984}(6401, \cdot)\) n/a 880 2
9984.2.bg \(\chi_{9984}(1409, \cdot)\) n/a 880 2
9984.2.bh \(\chi_{9984}(4031, \cdot)\) n/a 768 2
9984.2.bj \(\chi_{9984}(961, \cdot)\) n/a 448 2
9984.2.bm \(\chi_{9984}(1217, \cdot)\) n/a 896 2
9984.2.bn \(\chi_{9984}(6079, \cdot)\) n/a 448 2
9984.2.bq \(\chi_{9984}(3455, \cdot)\) n/a 880 2
9984.2.br \(\chi_{9984}(1153, \cdot)\) n/a 448 2
9984.2.bu \(\chi_{9984}(3071, \cdot)\) n/a 880 2
9984.2.bv \(\chi_{9984}(2305, \cdot)\) n/a 448 2
9984.2.bz \(\chi_{9984}(3839, \cdot)\) n/a 880 2
9984.2.ca \(\chi_{9984}(1921, \cdot)\) n/a 448 2
9984.2.cd \(\chi_{9984}(2687, \cdot)\) n/a 880 2
9984.2.cf \(\chi_{9984}(2465, \cdot)\) n/a 1760 4
9984.2.ch \(\chi_{9984}(2335, \cdot)\) n/a 896 4
9984.2.ci \(\chi_{9984}(2209, \cdot)\) n/a 896 4
9984.2.ck \(\chi_{9984}(1249, \cdot)\) n/a 768 4
9984.2.cn \(\chi_{9984}(287, \cdot)\) n/a 1536 4
9984.2.cp \(\chi_{9984}(1247, \cdot)\) n/a 1760 4
9984.2.cq \(\chi_{9984}(161, \cdot)\) n/a 1760 4
9984.2.cs \(\chi_{9984}(31, \cdot)\) n/a 896 4
9984.2.cu \(\chi_{9984}(5441, \cdot)\) n/a 1792 4
9984.2.cx \(\chi_{9984}(319, \cdot)\) n/a 896 4
9984.2.cz \(\chi_{9984}(4417, \cdot)\) n/a 896 4
9984.2.db \(\chi_{9984}(191, \cdot)\) n/a 1792 4
9984.2.dc \(\chi_{9984}(2177, \cdot)\) n/a 1760 4
9984.2.dd \(\chi_{9984}(1025, \cdot)\) n/a 1760 4
9984.2.dg \(\chi_{9984}(2047, \cdot)\) n/a 896 4
9984.2.dh \(\chi_{9984}(895, \cdot)\) n/a 896 4
9984.2.dl \(\chi_{9984}(3649, \cdot)\) n/a 896 4
9984.2.dn \(\chi_{9984}(959, \cdot)\) n/a 1792 4
9984.2.dp \(\chi_{9984}(5311, \cdot)\) n/a 896 4
9984.2.dq \(\chi_{9984}(449, \cdot)\) n/a 1792 4
9984.2.ds \(\chi_{9984}(625, \cdot)\) n/a 1536 8
9984.2.dt \(\chi_{9984}(623, \cdot)\) n/a 3552 8
9984.2.dw \(\chi_{9984}(593, \cdot)\) n/a 3552 8
9984.2.dx \(\chi_{9984}(655, \cdot)\) n/a 1792 8
9984.2.ea \(\chi_{9984}(785, \cdot)\) n/a 3552 8
9984.2.eb \(\chi_{9984}(463, \cdot)\) n/a 1792 8
9984.2.ee \(\chi_{9984}(911, \cdot)\) n/a 3072 8
9984.2.ef \(\chi_{9984}(337, \cdot)\) n/a 1792 8
9984.2.ej \(\chi_{9984}(799, \cdot)\) n/a 1792 8
9984.2.el \(\chi_{9984}(929, \cdot)\) n/a 3520 8
9984.2.en \(\chi_{9984}(1439, \cdot)\) n/a 3520 8
9984.2.ep \(\chi_{9984}(95, \cdot)\) n/a 3520 8
9984.2.eq \(\chi_{9984}(673, \cdot)\) n/a 1792 8
9984.2.es \(\chi_{9984}(289, \cdot)\) n/a 1792 8
9984.2.eu \(\chi_{9984}(223, \cdot)\) n/a 1792 8
9984.2.ew \(\chi_{9984}(353, \cdot)\) n/a 3520 8
9984.2.ey \(\chi_{9984}(281, \cdot)\) None 0 16
9984.2.fa \(\chi_{9984}(151, \cdot)\) None 0 16
9984.2.fc \(\chi_{9984}(599, \cdot)\) None 0 16
9984.2.fd \(\chi_{9984}(311, \cdot)\) None 0 16
9984.2.fg \(\chi_{9984}(313, \cdot)\) None 0 16
9984.2.fh \(\chi_{9984}(25, \cdot)\) None 0 16
9984.2.fl \(\chi_{9984}(343, \cdot)\) None 0 16
9984.2.fn \(\chi_{9984}(473, \cdot)\) None 0 16
9984.2.fq \(\chi_{9984}(335, \cdot)\) n/a 7104 16
9984.2.fr \(\chi_{9984}(529, \cdot)\) n/a 3584 16
9984.2.fu \(\chi_{9984}(847, \cdot)\) n/a 3584 16
9984.2.fv \(\chi_{9984}(305, \cdot)\) n/a 7104 16
9984.2.fy \(\chi_{9984}(175, \cdot)\) n/a 3584 16
9984.2.fz \(\chi_{9984}(977, \cdot)\) n/a 7104 16
9984.2.gc \(\chi_{9984}(49, \cdot)\) n/a 3584 16
9984.2.gd \(\chi_{9984}(815, \cdot)\) n/a 7104 16
9984.2.ge \(\chi_{9984}(187, \cdot)\) n/a 28672 32
9984.2.gi \(\chi_{9984}(157, \cdot)\) n/a 24576 32
9984.2.gj \(\chi_{9984}(181, \cdot)\) n/a 28672 32
9984.2.gk \(\chi_{9984}(499, \cdot)\) n/a 28672 32
9984.2.gn \(\chi_{9984}(5, \cdot)\) n/a 57216 32
9984.2.go \(\chi_{9984}(131, \cdot)\) n/a 49152 32
9984.2.gp \(\chi_{9984}(155, \cdot)\) n/a 57216 32
9984.2.gt \(\chi_{9984}(317, \cdot)\) n/a 57216 32
9984.2.gu \(\chi_{9984}(487, \cdot)\) None 0 32
9984.2.gw \(\chi_{9984}(41, \cdot)\) None 0 32
9984.2.ha \(\chi_{9984}(121, \cdot)\) None 0 32
9984.2.hb \(\chi_{9984}(217, \cdot)\) None 0 32
9984.2.he \(\chi_{9984}(23, \cdot)\) None 0 32
9984.2.hf \(\chi_{9984}(263, \cdot)\) None 0 32
9984.2.hh \(\chi_{9984}(137, \cdot)\) None 0 32
9984.2.hj \(\chi_{9984}(7, \cdot)\) None 0 32
9984.2.hk \(\chi_{9984}(245, \cdot)\) n/a 114432 64
9984.2.ho \(\chi_{9984}(179, \cdot)\) n/a 114432 64
9984.2.hp \(\chi_{9984}(35, \cdot)\) n/a 114432 64
9984.2.hq \(\chi_{9984}(149, \cdot)\) n/a 114432 64
9984.2.ht \(\chi_{9984}(19, \cdot)\) n/a 57344 64
9984.2.hu \(\chi_{9984}(205, \cdot)\) n/a 57344 64
9984.2.hv \(\chi_{9984}(61, \cdot)\) n/a 57344 64
9984.2.hz \(\chi_{9984}(115, \cdot)\) n/a 57344 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9984))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9984)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1664))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2496))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3328))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4992))\)\(^{\oplus 2}\)