# Properties

 Label 5166.2 Level 5166 Weight 2 Dimension 183320 Nonzero newspaces 80 Sturm bound 2903040

## Defining parameters

 Level: $$N$$ = $$5166 = 2 \cdot 3^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$2903040$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5166))$$.

Total New Old
Modular forms 733440 183320 550120
Cusp forms 718081 183320 534761
Eisenstein series 15359 0 15359

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5166))$$

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
5166.2.a $$\chi_{5166}(1, \cdot)$$ 5166.2.a.a 1 1
5166.2.a.b 1
5166.2.a.c 1
5166.2.a.d 1
5166.2.a.e 1
5166.2.a.f 1
5166.2.a.g 1
5166.2.a.h 1
5166.2.a.i 1
5166.2.a.j 1
5166.2.a.k 1
5166.2.a.l 1
5166.2.a.m 1
5166.2.a.n 1
5166.2.a.o 1
5166.2.a.p 1
5166.2.a.q 1
5166.2.a.r 1
5166.2.a.s 1
5166.2.a.t 1
5166.2.a.u 1
5166.2.a.v 1
5166.2.a.w 1
5166.2.a.x 1
5166.2.a.y 1
5166.2.a.z 1
5166.2.a.ba 1
5166.2.a.bb 1
5166.2.a.bc 1
5166.2.a.bd 1
5166.2.a.be 1
5166.2.a.bf 1
5166.2.a.bg 1
5166.2.a.bh 1
5166.2.a.bi 1
5166.2.a.bj 1
5166.2.a.bk 1
5166.2.a.bl 1
5166.2.a.bm 1
5166.2.a.bn 2
5166.2.a.bo 2
5166.2.a.bp 2
5166.2.a.bq 2
5166.2.a.br 2
5166.2.a.bs 2
5166.2.a.bt 3
5166.2.a.bu 3
5166.2.a.bv 3
5166.2.a.bw 3
5166.2.a.bx 4
5166.2.a.by 5
5166.2.a.bz 7
5166.2.a.ca 7
5166.2.a.cb 7
5166.2.a.cc 7
5166.2.f $$\chi_{5166}(1639, \cdot)$$ n/a 104 1
5166.2.g $$\chi_{5166}(3527, \cdot)$$ n/a 112 1
5166.2.h $$\chi_{5166}(5165, \cdot)$$ n/a 112 1
5166.2.i $$\chi_{5166}(247, \cdot)$$ n/a 640 2
5166.2.j $$\chi_{5166}(1723, \cdot)$$ n/a 480 2
5166.2.k $$\chi_{5166}(739, \cdot)$$ n/a 264 2
5166.2.l $$\chi_{5166}(1969, \cdot)$$ n/a 640 2
5166.2.m $$\chi_{5166}(1385, \cdot)$$ n/a 224 2
5166.2.n $$\chi_{5166}(3025, \cdot)$$ n/a 212 2
5166.2.q $$\chi_{5166}(379, \cdot)$$ n/a 416 4
5166.2.v $$\chi_{5166}(1721, \cdot)$$ n/a 672 2
5166.2.w $$\chi_{5166}(983, \cdot)$$ n/a 672 2
5166.2.x $$\chi_{5166}(1475, \cdot)$$ n/a 224 2
5166.2.y $$\chi_{5166}(2789, \cdot)$$ n/a 208 2
5166.2.z $$\chi_{5166}(163, \cdot)$$ n/a 280 2
5166.2.ba $$\chi_{5166}(3361, \cdot)$$ n/a 504 2
5166.2.bb $$\chi_{5166}(3281, \cdot)$$ n/a 640 2
5166.2.bc $$\chi_{5166}(655, \cdot)$$ n/a 672 2
5166.2.bd $$\chi_{5166}(83, \cdot)$$ n/a 640 2
5166.2.bq $$\chi_{5166}(1067, \cdot)$$ n/a 640 2
5166.2.br $$\chi_{5166}(3607, \cdot)$$ n/a 672 2
5166.2.bs $$\chi_{5166}(2705, \cdot)$$ n/a 672 2
5166.2.bu $$\chi_{5166}(55, \cdot)$$ n/a 560 4
5166.2.bv $$\chi_{5166}(2843, \cdot)$$ n/a 336 4
5166.2.bx $$\chi_{5166}(1007, \cdot)$$ n/a 448 4
5166.2.by $$\chi_{5166}(2519, \cdot)$$ n/a 448 4
5166.2.bz $$\chi_{5166}(127, \cdot)$$ n/a 416 4
5166.2.ce $$\chi_{5166}(173, \cdot)$$ n/a 1344 4
5166.2.cf $$\chi_{5166}(319, \cdot)$$ n/a 1344 4
5166.2.cm $$\chi_{5166}(1549, \cdot)$$ n/a 560 4
5166.2.cn $$\chi_{5166}(337, \cdot)$$ n/a 1008 4
5166.2.co $$\chi_{5166}(2041, \cdot)$$ n/a 1344 4
5166.2.cp $$\chi_{5166}(1139, \cdot)$$ n/a 1344 4
5166.2.cq $$\chi_{5166}(647, \cdot)$$ n/a 448 4
5166.2.cr $$\chi_{5166}(419, \cdot)$$ n/a 1344 4
5166.2.cu $$\chi_{5166}(961, \cdot)$$ n/a 2688 8
5166.2.cv $$\chi_{5166}(37, \cdot)$$ n/a 1120 8
5166.2.cw $$\chi_{5166}(715, \cdot)$$ n/a 2016 8
5166.2.cx $$\chi_{5166}(529, \cdot)$$ n/a 2688 8
5166.2.da $$\chi_{5166}(1765, \cdot)$$ n/a 848 8
5166.2.db $$\chi_{5166}(125, \cdot)$$ n/a 896 8
5166.2.dc $$\chi_{5166}(817, \cdot)$$ n/a 2688 8
5166.2.de $$\chi_{5166}(137, \cdot)$$ n/a 2688 8
5166.2.dh $$\chi_{5166}(683, \cdot)$$ n/a 896 8
5166.2.di $$\chi_{5166}(407, \cdot)$$ n/a 2016 8
5166.2.dl $$\chi_{5166}(325, \cdot)$$ n/a 1120 8
5166.2.dm $$\chi_{5166}(601, \cdot)$$ n/a 2688 8
5166.2.dp $$\chi_{5166}(355, \cdot)$$ n/a 2688 8
5166.2.dr $$\chi_{5166}(191, \cdot)$$ n/a 2688 8
5166.2.ds $$\chi_{5166}(1193, \cdot)$$ n/a 2688 8
5166.2.dt $$\chi_{5166}(2095, \cdot)$$ n/a 2688 8
5166.2.du $$\chi_{5166}(59, \cdot)$$ n/a 2688 8
5166.2.eh $$\chi_{5166}(461, \cdot)$$ n/a 2688 8
5166.2.ei $$\chi_{5166}(25, \cdot)$$ n/a 2688 8
5166.2.ej $$\chi_{5166}(857, \cdot)$$ n/a 2688 8
5166.2.ek $$\chi_{5166}(925, \cdot)$$ n/a 2016 8
5166.2.el $$\chi_{5166}(865, \cdot)$$ n/a 1120 8
5166.2.em $$\chi_{5166}(215, \cdot)$$ n/a 896 8
5166.2.en $$\chi_{5166}(269, \cdot)$$ n/a 896 8
5166.2.eo $$\chi_{5166}(353, \cdot)$$ n/a 2688 8
5166.2.ep $$\chi_{5166}(209, \cdot)$$ n/a 2688 8
5166.2.ev $$\chi_{5166}(71, \cdot)$$ n/a 1344 16
5166.2.ew $$\chi_{5166}(181, \cdot)$$ n/a 2240 16
5166.2.fa $$\chi_{5166}(923, \cdot)$$ n/a 5376 16
5166.2.fb $$\chi_{5166}(143, \cdot)$$ n/a 1792 16
5166.2.fc $$\chi_{5166}(5, \cdot)$$ n/a 5376 16
5166.2.fd $$\chi_{5166}(121, \cdot)$$ n/a 5376 16
5166.2.fe $$\chi_{5166}(43, \cdot)$$ n/a 4032 16
5166.2.ff $$\chi_{5166}(289, \cdot)$$ n/a 2240 16
5166.2.fm $$\chi_{5166}(1087, \cdot)$$ n/a 5376 16
5166.2.fn $$\chi_{5166}(185, \cdot)$$ n/a 5376 16
5166.2.fo $$\chi_{5166}(65, \cdot)$$ n/a 10752 32
5166.2.fq $$\chi_{5166}(229, \cdot)$$ n/a 10752 32
5166.2.ft $$\chi_{5166}(13, \cdot)$$ n/a 10752 32
5166.2.fu $$\chi_{5166}(19, \cdot)$$ n/a 4480 32
5166.2.fx $$\chi_{5166}(29, \cdot)$$ n/a 8064 32
5166.2.fy $$\chi_{5166}(53, \cdot)$$ n/a 3584 32
5166.2.gb $$\chi_{5166}(11, \cdot)$$ n/a 10752 32
5166.2.gd $$\chi_{5166}(157, \cdot)$$ n/a 10752 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5166))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5166)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(82))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(123))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(246))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(287))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(369))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(574))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(738))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(861))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1722))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2583))$$$$^{\oplus 2}$$