Properties

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

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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

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