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Properties

Label 6270.2
Level 6270
Weight 2
Dimension 232351
Nonzero newspaces 72
Sturm bound 4147200

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Defining parameters

Level: \( N \) = \( 6270 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(4147200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6270))\).

Total New Old
Modular forms 1048320 232351 815969
Cusp forms 1025281 232351 792930
Eisenstein series 23039 0 23039

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6270))\)

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
6270.2.a \(\chi_{6270}(1, \cdot)\) 6270.2.a.a 1 1
6270.2.a.b 1
6270.2.a.c 1
6270.2.a.d 1
6270.2.a.e 1
6270.2.a.f 1
6270.2.a.g 1
6270.2.a.h 1
6270.2.a.i 1
6270.2.a.j 1
6270.2.a.k 1
6270.2.a.l 1
6270.2.a.m 1
6270.2.a.n 1
6270.2.a.o 1
6270.2.a.p 1
6270.2.a.q 1
6270.2.a.r 1
6270.2.a.s 2
6270.2.a.t 2
6270.2.a.u 2
6270.2.a.v 2
6270.2.a.w 2
6270.2.a.x 2
6270.2.a.y 2
6270.2.a.z 2
6270.2.a.ba 3
6270.2.a.bb 3
6270.2.a.bc 3
6270.2.a.bd 3
6270.2.a.be 3
6270.2.a.bf 3
6270.2.a.bg 3
6270.2.a.bh 3
6270.2.a.bi 3
6270.2.a.bj 3
6270.2.a.bk 4
6270.2.a.bl 4
6270.2.a.bm 4
6270.2.a.bn 4
6270.2.a.bo 4
6270.2.a.bp 4
6270.2.a.bq 5
6270.2.a.br 5
6270.2.a.bs 5
6270.2.a.bt 5
6270.2.a.bu 5
6270.2.a.bv 6
6270.2.b \(\chi_{6270}(2509, \cdot)\) n/a 184 1
6270.2.d \(\chi_{6270}(4751, \cdot)\) n/a 288 1
6270.2.g \(\chi_{6270}(5851, \cdot)\) n/a 160 1
6270.2.i \(\chi_{6270}(5699, \cdot)\) n/a 400 1
6270.2.j \(\chi_{6270}(3191, \cdot)\) n/a 272 1
6270.2.l \(\chi_{6270}(2089, \cdot)\) n/a 240 1
6270.2.o \(\chi_{6270}(989, \cdot)\) n/a 432 1
6270.2.q \(\chi_{6270}(2971, \cdot)\) n/a 256 2
6270.2.v \(\chi_{6270}(1253, \cdot)\) n/a 960 2
6270.2.w \(\chi_{6270}(2773, \cdot)\) n/a 400 2
6270.2.x \(\chi_{6270}(4333, \cdot)\) n/a 432 2
6270.2.y \(\chi_{6270}(1673, \cdot)\) n/a 720 2
6270.2.z \(\chi_{6270}(2281, \cdot)\) n/a 576 4
6270.2.ba \(\chi_{6270}(749, \cdot)\) n/a 800 2
6270.2.bc \(\chi_{6270}(901, \cdot)\) n/a 320 2
6270.2.bf \(\chi_{6270}(1451, \cdot)\) n/a 640 2
6270.2.bh \(\chi_{6270}(1189, \cdot)\) n/a 400 2
6270.2.bj \(\chi_{6270}(3959, \cdot)\) n/a 960 2
6270.2.bm \(\chi_{6270}(3409, \cdot)\) n/a 480 2
6270.2.bo \(\chi_{6270}(221, \cdot)\) n/a 544 2
6270.2.bp \(\chi_{6270}(1651, \cdot)\) n/a 816 6
6270.2.bs \(\chi_{6270}(1559, \cdot)\) n/a 1728 4
6270.2.bt \(\chi_{6270}(2659, \cdot)\) n/a 960 4
6270.2.bv \(\chi_{6270}(911, \cdot)\) n/a 1280 4
6270.2.by \(\chi_{6270}(1709, \cdot)\) n/a 1920 4
6270.2.ca \(\chi_{6270}(151, \cdot)\) n/a 640 4
6270.2.cb \(\chi_{6270}(761, \cdot)\) n/a 1152 4
6270.2.cd \(\chi_{6270}(229, \cdot)\) n/a 864 4
6270.2.cf \(\chi_{6270}(1057, \cdot)\) n/a 800 4
6270.2.cg \(\chi_{6270}(2573, \cdot)\) n/a 1920 4
6270.2.ch \(\chi_{6270}(353, \cdot)\) n/a 1600 4
6270.2.ci \(\chi_{6270}(1033, \cdot)\) n/a 960 4
6270.2.cn \(\chi_{6270}(691, \cdot)\) n/a 1280 8
6270.2.cp \(\chi_{6270}(329, \cdot)\) n/a 2880 6
6270.2.cs \(\chi_{6270}(1211, \cdot)\) n/a 1584 6
6270.2.ct \(\chi_{6270}(109, \cdot)\) n/a 1440 6
6270.2.cw \(\chi_{6270}(199, \cdot)\) n/a 1200 6
6270.2.cx \(\chi_{6270}(131, \cdot)\) n/a 1920 6
6270.2.da \(\chi_{6270}(241, \cdot)\) n/a 960 6
6270.2.db \(\chi_{6270}(89, \cdot)\) n/a 2400 6
6270.2.dd \(\chi_{6270}(533, \cdot)\) n/a 3456 8
6270.2.de \(\chi_{6270}(343, \cdot)\) n/a 1728 8
6270.2.df \(\chi_{6270}(37, \cdot)\) n/a 1920 8
6270.2.dg \(\chi_{6270}(227, \cdot)\) n/a 3840 8
6270.2.dm \(\chi_{6270}(521, \cdot)\) n/a 2560 8
6270.2.do \(\chi_{6270}(259, \cdot)\) n/a 1920 8
6270.2.dp \(\chi_{6270}(239, \cdot)\) n/a 3840 8
6270.2.dt \(\chi_{6270}(49, \cdot)\) n/a 1920 8
6270.2.dv \(\chi_{6270}(1151, \cdot)\) n/a 2560 8
6270.2.dw \(\chi_{6270}(601, \cdot)\) n/a 1280 8
6270.2.dy \(\chi_{6270}(179, \cdot)\) n/a 3840 8
6270.2.eb \(\chi_{6270}(43, \cdot)\) n/a 2880 12
6270.2.ec \(\chi_{6270}(23, \cdot)\) n/a 4800 12
6270.2.ee \(\chi_{6270}(67, \cdot)\) n/a 2400 12
6270.2.eh \(\chi_{6270}(527, \cdot)\) n/a 5760 12
6270.2.ei \(\chi_{6270}(301, \cdot)\) n/a 3840 24
6270.2.en \(\chi_{6270}(7, \cdot)\) n/a 3840 16
6270.2.eo \(\chi_{6270}(467, \cdot)\) n/a 7680 16
6270.2.ep \(\chi_{6270}(107, \cdot)\) n/a 7680 16
6270.2.eq \(\chi_{6270}(103, \cdot)\) n/a 3840 16
6270.2.es \(\chi_{6270}(59, \cdot)\) n/a 11520 24
6270.2.et \(\chi_{6270}(211, \cdot)\) n/a 3840 24
6270.2.ew \(\chi_{6270}(101, \cdot)\) n/a 7680 24
6270.2.ex \(\chi_{6270}(169, \cdot)\) n/a 5760 24
6270.2.fa \(\chi_{6270}(79, \cdot)\) n/a 5760 24
6270.2.fb \(\chi_{6270}(71, \cdot)\) n/a 7680 24
6270.2.fe \(\chi_{6270}(149, \cdot)\) n/a 11520 24
6270.2.fg \(\chi_{6270}(167, \cdot)\) n/a 23040 48
6270.2.fj \(\chi_{6270}(97, \cdot)\) n/a 11520 48
6270.2.fl \(\chi_{6270}(47, \cdot)\) n/a 23040 48
6270.2.fm \(\chi_{6270}(73, \cdot)\) n/a 11520 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6270))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6270)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1045))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1254))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2090))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3135))\)\(^{\oplus 2}\)