Properties

Label 5184.2
Level 5184
Weight 2
Dimension 330544
Nonzero newspaces 32
Sturm bound 2985984

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Defining parameters

Level: \( N \) = \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(2985984\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5184))\).

Total New Old
Modular forms 754272 333008 421264
Cusp forms 738721 330544 408177
Eisenstein series 15551 2464 13087

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5184))\)

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
5184.2.a \(\chi_{5184}(1, \cdot)\) 5184.2.a.a 1 1
5184.2.a.b 1
5184.2.a.c 1
5184.2.a.d 1
5184.2.a.e 1
5184.2.a.f 1
5184.2.a.g 1
5184.2.a.h 1
5184.2.a.i 1
5184.2.a.j 1
5184.2.a.k 1
5184.2.a.l 1
5184.2.a.m 1
5184.2.a.n 1
5184.2.a.o 1
5184.2.a.p 1
5184.2.a.q 1
5184.2.a.r 1
5184.2.a.s 1
5184.2.a.t 1
5184.2.a.u 1
5184.2.a.v 1
5184.2.a.w 1
5184.2.a.x 1
5184.2.a.y 1
5184.2.a.z 1
5184.2.a.ba 1
5184.2.a.bb 1
5184.2.a.bc 1
5184.2.a.bd 1
5184.2.a.be 1
5184.2.a.bf 1
5184.2.a.bg 2
5184.2.a.bh 2
5184.2.a.bi 2
5184.2.a.bj 2
5184.2.a.bk 2
5184.2.a.bl 2
5184.2.a.bm 2
5184.2.a.bn 2
5184.2.a.bo 2
5184.2.a.bp 2
5184.2.a.bq 2
5184.2.a.br 2
5184.2.a.bs 2
5184.2.a.bt 2
5184.2.a.bu 2
5184.2.a.bv 2
5184.2.a.bw 2
5184.2.a.bx 2
5184.2.a.by 2
5184.2.a.bz 2
5184.2.a.ca 2
5184.2.a.cb 2
5184.2.a.cc 4
5184.2.a.cd 4
5184.2.a.ce 4
5184.2.a.cf 4
5184.2.c \(\chi_{5184}(5183, \cdot)\) 5184.2.c.a 2 1
5184.2.c.b 2
5184.2.c.c 2
5184.2.c.d 2
5184.2.c.e 4
5184.2.c.f 4
5184.2.c.g 4
5184.2.c.h 8
5184.2.c.i 8
5184.2.c.j 8
5184.2.c.k 8
5184.2.c.l 16
5184.2.c.m 24
5184.2.d \(\chi_{5184}(2593, \cdot)\) 5184.2.d.a 4 1
5184.2.d.b 4
5184.2.d.c 4
5184.2.d.d 4
5184.2.d.e 4
5184.2.d.f 4
5184.2.d.g 4
5184.2.d.h 4
5184.2.d.i 4
5184.2.d.j 4
5184.2.d.k 4
5184.2.d.l 4
5184.2.d.m 4
5184.2.d.n 4
5184.2.d.o 8
5184.2.d.p 8
5184.2.d.q 12
5184.2.d.r 12
5184.2.f \(\chi_{5184}(2591, \cdot)\) 5184.2.f.a 16 1
5184.2.f.b 16
5184.2.f.c 16
5184.2.f.d 16
5184.2.f.e 16
5184.2.f.f 16
5184.2.i \(\chi_{5184}(1729, \cdot)\) n/a 188 2
5184.2.k \(\chi_{5184}(1297, \cdot)\) n/a 184 2
5184.2.l \(\chi_{5184}(1295, \cdot)\) n/a 184 2
5184.2.p \(\chi_{5184}(863, \cdot)\) n/a 192 2
5184.2.r \(\chi_{5184}(865, \cdot)\) n/a 192 2
5184.2.s \(\chi_{5184}(1727, \cdot)\) n/a 188 2
5184.2.v \(\chi_{5184}(649, \cdot)\) None 0 4
5184.2.w \(\chi_{5184}(647, \cdot)\) None 0 4
5184.2.y \(\chi_{5184}(577, \cdot)\) n/a 420 6
5184.2.z \(\chi_{5184}(431, \cdot)\) n/a 376 4
5184.2.bc \(\chi_{5184}(433, \cdot)\) n/a 376 4
5184.2.be \(\chi_{5184}(325, \cdot)\) n/a 3040 8
5184.2.bf \(\chi_{5184}(323, \cdot)\) n/a 3040 8
5184.2.bj \(\chi_{5184}(289, \cdot)\) n/a 432 6
5184.2.bl \(\chi_{5184}(287, \cdot)\) n/a 432 6
5184.2.bm \(\chi_{5184}(575, \cdot)\) n/a 420 6
5184.2.bo \(\chi_{5184}(217, \cdot)\) None 0 8
5184.2.br \(\chi_{5184}(215, \cdot)\) None 0 8
5184.2.bs \(\chi_{5184}(193, \cdot)\) n/a 3852 18
5184.2.bt \(\chi_{5184}(145, \cdot)\) n/a 840 12
5184.2.bw \(\chi_{5184}(143, \cdot)\) n/a 840 12
5184.2.by \(\chi_{5184}(107, \cdot)\) n/a 6112 16
5184.2.bz \(\chi_{5184}(109, \cdot)\) n/a 6112 16
5184.2.cd \(\chi_{5184}(95, \cdot)\) n/a 3888 18
5184.2.cf \(\chi_{5184}(97, \cdot)\) n/a 3888 18
5184.2.cg \(\chi_{5184}(191, \cdot)\) n/a 3852 18
5184.2.cj \(\chi_{5184}(71, \cdot)\) None 0 24
5184.2.ck \(\chi_{5184}(73, \cdot)\) None 0 24
5184.2.cm \(\chi_{5184}(47, \cdot)\) n/a 7704 36
5184.2.cp \(\chi_{5184}(49, \cdot)\) n/a 7704 36
5184.2.cq \(\chi_{5184}(37, \cdot)\) n/a 13728 48
5184.2.ct \(\chi_{5184}(35, \cdot)\) n/a 13728 48
5184.2.cu \(\chi_{5184}(23, \cdot)\) None 0 72
5184.2.cx \(\chi_{5184}(25, \cdot)\) None 0 72
5184.2.cy \(\chi_{5184}(13, \cdot)\) n/a 124128 144
5184.2.db \(\chi_{5184}(11, \cdot)\) n/a 124128 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5184))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5184)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(864))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1296))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2592))\)\(^{\oplus 2}\)