## 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

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