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Properties

Label 5586.2
Level 5586
Weight 2
Dimension 202004
Nonzero newspaces 64
Sturm bound 3386880

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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 available 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

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