## Defining parameters

 Level: $$N$$ = $$5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$3386880$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5586))$$.

Total New Old
Modular forms 855360 202004 653356
Cusp forms 838081 202004 636077
Eisenstein series 17279 0 17279

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5586))$$

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
5586.2.a $$\chi_{5586}(1, \cdot)$$ 5586.2.a.a 1 1
5586.2.a.b 1
5586.2.a.c 1
5586.2.a.d 1
5586.2.a.e 1
5586.2.a.f 1
5586.2.a.g 1
5586.2.a.h 1
5586.2.a.i 1
5586.2.a.j 1
5586.2.a.k 1
5586.2.a.l 1
5586.2.a.m 1
5586.2.a.n 1
5586.2.a.o 1
5586.2.a.p 1
5586.2.a.q 1
5586.2.a.r 1
5586.2.a.s 1
5586.2.a.t 1
5586.2.a.u 1
5586.2.a.v 1
5586.2.a.w 1
5586.2.a.x 1
5586.2.a.y 1
5586.2.a.z 1
5586.2.a.ba 1
5586.2.a.bb 1
5586.2.a.bc 2
5586.2.a.bd 2
5586.2.a.be 2
5586.2.a.bf 2
5586.2.a.bg 2
5586.2.a.bh 2
5586.2.a.bi 2
5586.2.a.bj 2
5586.2.a.bk 2
5586.2.a.bl 2
5586.2.a.bm 2
5586.2.a.bn 2
5586.2.a.bo 2
5586.2.a.bp 2
5586.2.a.bq 2
5586.2.a.br 2
5586.2.a.bs 3
5586.2.a.bt 3
5586.2.a.bu 3
5586.2.a.bv 3
5586.2.a.bw 4
5586.2.a.bx 4
5586.2.a.by 4
5586.2.a.bz 4
5586.2.a.ca 4
5586.2.a.cb 4
5586.2.a.cc 6
5586.2.a.cd 6
5586.2.a.ce 8
5586.2.a.cf 8
5586.2.b $$\chi_{5586}(4901, \cdot)$$ n/a 272 1
5586.2.e $$\chi_{5586}(1861, \cdot)$$ n/a 136 1
5586.2.f $$\chi_{5586}(4409, \cdot)$$ n/a 240 1
5586.2.i $$\chi_{5586}(961, \cdot)$$ n/a 264 2
5586.2.j $$\chi_{5586}(1255, \cdot)$$ n/a 240 2
5586.2.k $$\chi_{5586}(2059, \cdot)$$ n/a 276 2
5586.2.l $$\chi_{5586}(3313, \cdot)$$ n/a 264 2
5586.2.m $$\chi_{5586}(2383, \cdot)$$ n/a 264 2
5586.2.p $$\chi_{5586}(4097, \cdot)$$ n/a 536 2
5586.2.r $$\chi_{5586}(881, \cdot)$$ n/a 528 2
5586.2.u $$\chi_{5586}(3155, \cdot)$$ n/a 480 2
5586.2.w $$\chi_{5586}(1109, \cdot)$$ n/a 536 2
5586.2.ba $$\chi_{5586}(2843, \cdot)$$ n/a 544 2
5586.2.bc $$\chi_{5586}(31, \cdot)$$ n/a 264 2
5586.2.be $$\chi_{5586}(607, \cdot)$$ n/a 264 2
5586.2.bf $$\chi_{5586}(569, \cdot)$$ n/a 536 2
5586.2.bh $$\chi_{5586}(863, \cdot)$$ n/a 536 2
5586.2.bj $$\chi_{5586}(2155, \cdot)$$ n/a 272 2
5586.2.bn $$\chi_{5586}(4343, \cdot)$$ n/a 536 2
5586.2.bo $$\chi_{5586}(799, \cdot)$$ n/a 1008 6
5586.2.bp $$\chi_{5586}(883, \cdot)$$ n/a 816 6
5586.2.bq $$\chi_{5586}(1537, \cdot)$$ n/a 804 6
5586.2.br $$\chi_{5586}(655, \cdot)$$ n/a 804 6
5586.2.bu $$\chi_{5586}(419, \cdot)$$ n/a 2016 6
5586.2.bv $$\chi_{5586}(265, \cdot)$$ n/a 1104 6
5586.2.by $$\chi_{5586}(113, \cdot)$$ n/a 2256 6
5586.2.cb $$\chi_{5586}(803, \cdot)$$ n/a 1596 6
5586.2.cc $$\chi_{5586}(851, \cdot)$$ n/a 1596 6
5586.2.cf $$\chi_{5586}(97, \cdot)$$ n/a 792 6
5586.2.ci $$\chi_{5586}(325, \cdot)$$ n/a 804 6
5586.2.cj $$\chi_{5586}(215, \cdot)$$ n/a 1596 6
5586.2.ck $$\chi_{5586}(1439, \cdot)$$ n/a 1596 6
5586.2.cn $$\chi_{5586}(1079, \cdot)$$ n/a 1644 6
5586.2.co $$\chi_{5586}(587, \cdot)$$ n/a 1608 6
5586.2.cr $$\chi_{5586}(1207, \cdot)$$ n/a 804 6
5586.2.cu $$\chi_{5586}(121, \cdot)$$ n/a 2256 12
5586.2.cv $$\chi_{5586}(463, \cdot)$$ n/a 2208 12
5586.2.cw $$\chi_{5586}(457, \cdot)$$ n/a 2016 12
5586.2.cx $$\chi_{5586}(163, \cdot)$$ n/a 2256 12
5586.2.cy $$\chi_{5586}(353, \cdot)$$ n/a 4464 12
5586.2.dc $$\chi_{5586}(559, \cdot)$$ n/a 2208 12
5586.2.de $$\chi_{5586}(65, \cdot)$$ n/a 4464 12
5586.2.dg $$\chi_{5586}(683, \cdot)$$ n/a 4464 12
5586.2.dh $$\chi_{5586}(493, \cdot)$$ n/a 2256 12
5586.2.dj $$\chi_{5586}(103, \cdot)$$ n/a 2256 12
5586.2.dl $$\chi_{5586}(407, \cdot)$$ n/a 4512 12
5586.2.dp $$\chi_{5586}(311, \cdot)$$ n/a 4464 12
5586.2.dr $$\chi_{5586}(647, \cdot)$$ n/a 4032 12
5586.2.du $$\chi_{5586}(83, \cdot)$$ n/a 4512 12
5586.2.dw $$\chi_{5586}(107, \cdot)$$ n/a 4464 12
5586.2.dz $$\chi_{5586}(145, \cdot)$$ n/a 2256 12
5586.2.ea $$\chi_{5586}(25, \cdot)$$ n/a 6696 36
5586.2.eb $$\chi_{5586}(43, \cdot)$$ n/a 6768 36
5586.2.ec $$\chi_{5586}(289, \cdot)$$ n/a 6696 36
5586.2.ed $$\chi_{5586}(241, \cdot)$$ n/a 6696 36
5586.2.eg $$\chi_{5586}(317, \cdot)$$ n/a 13464 36
5586.2.eh $$\chi_{5586}(17, \cdot)$$ n/a 13464 36
5586.2.ek $$\chi_{5586}(251, \cdot)$$ n/a 13392 36
5586.2.el $$\chi_{5586}(29, \cdot)$$ n/a 13392 36
5586.2.eq $$\chi_{5586}(13, \cdot)$$ n/a 6768 36
5586.2.et $$\chi_{5586}(355, \cdot)$$ n/a 6696 36
5586.2.ew $$\chi_{5586}(53, \cdot)$$ n/a 13464 36
5586.2.ex $$\chi_{5586}(5, \cdot)$$ n/a 13464 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5586))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5586)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(399))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(798))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(931))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1862))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2793))$$$$^{\oplus 2}$$