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Properties

Label 8730.2
Level 8730
Weight 2
Dimension 491462
Nonzero newspaces 110
Sturm bound 8128512

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Defining parameters

Level: \( N \) = \( 8730 = 2 \cdot 3^{2} \cdot 5 \cdot 97 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 110 \)
Sturm bound: \(8128512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8730))\).

Total New Old
Modular forms 2044416 491462 1552954
Cusp forms 2019841 491462 1528379
Eisenstein series 24575 0 24575

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8730))\)

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
8730.2.a \(\chi_{8730}(1, \cdot)\) 8730.2.a.a 1 1
8730.2.a.b 1
8730.2.a.c 1
8730.2.a.d 1
8730.2.a.e 1
8730.2.a.f 1
8730.2.a.g 1
8730.2.a.h 1
8730.2.a.i 1
8730.2.a.j 1
8730.2.a.k 1
8730.2.a.l 1
8730.2.a.m 1
8730.2.a.n 1
8730.2.a.o 1
8730.2.a.p 2
8730.2.a.q 2
8730.2.a.r 2
8730.2.a.s 2
8730.2.a.t 2
8730.2.a.u 2
8730.2.a.v 2
8730.2.a.w 2
8730.2.a.x 2
8730.2.a.y 3
8730.2.a.z 3
8730.2.a.ba 3
8730.2.a.bb 4
8730.2.a.bc 4
8730.2.a.bd 4
8730.2.a.be 4
8730.2.a.bf 4
8730.2.a.bg 4
8730.2.a.bh 4
8730.2.a.bi 5
8730.2.a.bj 5
8730.2.a.bk 5
8730.2.a.bl 5
8730.2.a.bm 5
8730.2.a.bn 6
8730.2.a.bo 6
8730.2.a.bp 6
8730.2.a.bq 6
8730.2.a.br 7
8730.2.a.bs 8
8730.2.a.bt 8
8730.2.a.bu 9
8730.2.a.bv 9
8730.2.d \(\chi_{8730}(2521, \cdot)\) n/a 166 1
8730.2.e \(\chi_{8730}(5239, \cdot)\) n/a 240 1
8730.2.h \(\chi_{8730}(7759, \cdot)\) n/a 244 1
8730.2.i \(\chi_{8730}(811, \cdot)\) n/a 324 2
8730.2.j \(\chi_{8730}(2911, \cdot)\) n/a 768 2
8730.2.k \(\chi_{8730}(61, \cdot)\) n/a 784 2
8730.2.l \(\chi_{8730}(5881, \cdot)\) n/a 784 2
8730.2.n \(\chi_{8730}(4193, \cdot)\) n/a 392 2
8730.2.o \(\chi_{8730}(2717, \cdot)\) n/a 384 2
8730.2.p \(\chi_{8730}(4969, \cdot)\) n/a 488 2
8730.2.q \(\chi_{8730}(2791, \cdot)\) n/a 332 2
8730.2.r \(\chi_{8730}(5237, \cdot)\) n/a 392 2
8730.2.x \(\chi_{8730}(2447, \cdot)\) n/a 392 2
8730.2.y \(\chi_{8730}(2461, \cdot)\) n/a 784 2
8730.2.z \(\chi_{8730}(2389, \cdot)\) n/a 1176 2
8730.2.be \(\chi_{8730}(4789, \cdot)\) n/a 488 2
8730.2.bf \(\chi_{8730}(1939, \cdot)\) n/a 1176 2
8730.2.bk \(\chi_{8730}(1129, \cdot)\) n/a 1176 2
8730.2.bn \(\chi_{8730}(5431, \cdot)\) n/a 784 2
8730.2.bo \(\chi_{8730}(2329, \cdot)\) n/a 1152 2
8730.2.bp \(\chi_{8730}(1711, \cdot)\) n/a 324 2
8730.2.bq \(\chi_{8730}(6049, \cdot)\) n/a 488 2
8730.2.bv \(\chi_{8730}(4621, \cdot)\) n/a 784 2
8730.2.bw \(\chi_{8730}(229, \cdot)\) n/a 1176 2
8730.2.bx \(\chi_{8730}(4039, \cdot)\) n/a 1176 2
8730.2.ca \(\chi_{8730}(3151, \cdot)\) n/a 664 4
8730.2.cd \(\chi_{8730}(1907, \cdot)\) n/a 784 4
8730.2.cf \(\chi_{8730}(2087, \cdot)\) n/a 784 4
8730.2.ch \(\chi_{8730}(4429, \cdot)\) n/a 976 4
8730.2.ci \(\chi_{8730}(5513, \cdot)\) n/a 2352 4
8730.2.cl \(\chi_{8730}(2807, \cdot)\) n/a 784 4
8730.2.cm \(\chi_{8730}(1433, \cdot)\) n/a 2352 4
8730.2.cp \(\chi_{8730}(857, \cdot)\) n/a 2352 4
8730.2.cq \(\chi_{8730}(617, \cdot)\) n/a 2352 4
8730.2.cr \(\chi_{8730}(1051, \cdot)\) n/a 1568 4
8730.2.cs \(\chi_{8730}(889, \cdot)\) n/a 2352 4
8730.2.ct \(\chi_{8730}(1517, \cdot)\) n/a 2352 4
8730.2.dg \(\chi_{8730}(1553, \cdot)\) n/a 2304 4
8730.2.dh \(\chi_{8730}(3527, \cdot)\) n/a 784 4
8730.2.di \(\chi_{8730}(2777, \cdot)\) n/a 2352 4
8730.2.dj \(\chi_{8730}(2419, \cdot)\) n/a 2352 4
8730.2.dk \(\chi_{8730}(2641, \cdot)\) n/a 1568 4
8730.2.dl \(\chi_{8730}(91, \cdot)\) n/a 648 4
8730.2.dm \(\chi_{8730}(469, \cdot)\) n/a 976 4
8730.2.dn \(\chi_{8730}(2059, \cdot)\) n/a 2352 4
8730.2.do \(\chi_{8730}(1471, \cdot)\) n/a 1568 4
8730.2.dp \(\chi_{8730}(353, \cdot)\) n/a 2352 4
8730.2.dq \(\chi_{8730}(2267, \cdot)\) n/a 784 4
8730.2.dr \(\chi_{8730}(1163, \cdot)\) n/a 2352 4
8730.2.dx \(\chi_{8730}(1283, \cdot)\) n/a 2352 4
8730.2.dy \(\chi_{8730}(1277, \cdot)\) n/a 784 4
8730.2.eb \(\chi_{8730}(1643, \cdot)\) n/a 2352 4
8730.2.ec \(\chi_{8730}(113, \cdot)\) n/a 2352 4
8730.2.ee \(\chi_{8730}(503, \cdot)\) n/a 1568 8
8730.2.eg \(\chi_{8730}(361, \cdot)\) n/a 1328 8
8730.2.ej \(\chi_{8730}(109, \cdot)\) n/a 1968 8
8730.2.el \(\chi_{8730}(467, \cdot)\) n/a 1568 8
8730.2.en \(\chi_{8730}(121, \cdot)\) n/a 3136 8
8730.2.ep \(\chi_{8730}(1789, \cdot)\) n/a 4704 8
8730.2.eq \(\chi_{8730}(1519, \cdot)\) n/a 4704 8
8730.2.et \(\chi_{8730}(379, \cdot)\) n/a 1952 8
8730.2.eu \(\chi_{8730}(227, \cdot)\) n/a 4704 8
8730.2.ex \(\chi_{8730}(287, \cdot)\) n/a 1568 8
8730.2.ez \(\chi_{8730}(203, \cdot)\) n/a 4704 8
8730.2.fa \(\chi_{8730}(1847, \cdot)\) n/a 4704 8
8730.2.fd \(\chi_{8730}(683, \cdot)\) n/a 1568 8
8730.2.ff \(\chi_{8730}(1703, \cdot)\) n/a 4704 8
8730.2.fg \(\chi_{8730}(767, \cdot)\) n/a 4704 8
8730.2.fi \(\chi_{8730}(47, \cdot)\) n/a 4704 8
8730.2.fk \(\chi_{8730}(3061, \cdot)\) n/a 1296 8
8730.2.fn \(\chi_{8730}(241, \cdot)\) n/a 3136 8
8730.2.fo \(\chi_{8730}(151, \cdot)\) n/a 3136 8
8730.2.fq \(\chi_{8730}(979, \cdot)\) n/a 4704 8
8730.2.fs \(\chi_{8730}(127, \cdot)\) n/a 3920 16
8730.2.fv \(\chi_{8730}(1241, \cdot)\) n/a 2176 16
8730.2.fw \(\chi_{8730}(989, \cdot)\) n/a 3136 16
8730.2.fz \(\chi_{8730}(343, \cdot)\) n/a 3920 16
8730.2.gb \(\chi_{8730}(533, \cdot)\) n/a 9408 16
8730.2.gd \(\chi_{8730}(473, \cdot)\) n/a 9408 16
8730.2.ge \(\chi_{8730}(437, \cdot)\) n/a 9408 16
8730.2.gh \(\chi_{8730}(53, \cdot)\) n/a 3136 16
8730.2.gi \(\chi_{8730}(79, \cdot)\) n/a 9408 16
8730.2.gl \(\chi_{8730}(661, \cdot)\) n/a 6272 16
8730.2.gn \(\chi_{8730}(289, \cdot)\) n/a 3936 16
8730.2.gp \(\chi_{8730}(49, \cdot)\) n/a 9408 16
8730.2.gq \(\chi_{8730}(571, \cdot)\) n/a 6272 16
8730.2.gs \(\chi_{8730}(631, \cdot)\) n/a 2592 16
8730.2.gv \(\chi_{8730}(31, \cdot)\) n/a 6272 16
8730.2.gw \(\chi_{8730}(169, \cdot)\) n/a 9408 16
8730.2.gy \(\chi_{8730}(557, \cdot)\) n/a 3136 16
8730.2.hb \(\chi_{8730}(677, \cdot)\) n/a 9408 16
8730.2.hc \(\chi_{8730}(167, \cdot)\) n/a 9408 16
8730.2.he \(\chi_{8730}(293, \cdot)\) n/a 9408 16
8730.2.hh \(\chi_{8730}(337, \cdot)\) n/a 18816 32
8730.2.hi \(\chi_{8730}(37, \cdot)\) n/a 7840 32
8730.2.hl \(\chi_{8730}(7, \cdot)\) n/a 18816 32
8730.2.hm \(\chi_{8730}(29, \cdot)\) n/a 18816 32
8730.2.ho \(\chi_{8730}(149, \cdot)\) n/a 18816 32
8730.2.hr \(\chi_{8730}(179, \cdot)\) n/a 6272 32
8730.2.hs \(\chi_{8730}(71, \cdot)\) n/a 4096 32
8730.2.hv \(\chi_{8730}(131, \cdot)\) n/a 12544 32
8730.2.hx \(\chi_{8730}(641, \cdot)\) n/a 12544 32
8730.2.hy \(\chi_{8730}(373, \cdot)\) n/a 18816 32
8730.2.ib \(\chi_{8730}(217, \cdot)\) n/a 7840 32
8730.2.ic \(\chi_{8730}(67, \cdot)\) n/a 18816 32
8730.2.if \(\chi_{8730}(277, \cdot)\) n/a 18816 32
8730.2.ig \(\chi_{8730}(41, \cdot)\) n/a 12544 32
8730.2.ij \(\chi_{8730}(59, \cdot)\) n/a 18816 32
8730.2.ik \(\chi_{8730}(13, \cdot)\) n/a 18816 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8730))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8730)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(97))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(194))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(291))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(485))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(582))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(873))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(970))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1455))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1746))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2910))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4365))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8730))\)\(^{\oplus 1}\)