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Properties

Label 6223.2
Level 6223
Weight 2
Dimension 1510455
Nonzero newspaces 144
Sturm bound 6322176

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Defining parameters

Level: \( N \) = \( 6223 = 7^{2} \cdot 127 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 144 \)
Sturm bound: \(6322176\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6223))\).

Total New Old
Modular forms 1588104 1522579 65525
Cusp forms 1572985 1510455 62530
Eisenstein series 15119 12124 2995

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6223))\)

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
6223.2.a \(\chi_{6223}(1, \cdot)\) 6223.2.a.a 1 1
6223.2.a.b 1
6223.2.a.c 2
6223.2.a.d 2
6223.2.a.e 3
6223.2.a.f 4
6223.2.a.g 4
6223.2.a.h 7
6223.2.a.i 12
6223.2.a.j 15
6223.2.a.k 16
6223.2.a.l 20
6223.2.a.m 26
6223.2.a.n 34
6223.2.a.o 38
6223.2.a.p 38
6223.2.a.q 40
6223.2.a.r 40
6223.2.a.s 54
6223.2.a.t 74
6223.2.d \(\chi_{6223}(6222, \cdot)\) n/a 424 1
6223.2.e \(\chi_{6223}(2774, \cdot)\) n/a 844 2
6223.2.f \(\chi_{6223}(128, \cdot)\) n/a 840 2
6223.2.g \(\chi_{6223}(361, \cdot)\) n/a 844 2
6223.2.h \(\chi_{6223}(2647, \cdot)\) n/a 866 2
6223.2.k \(\chi_{6223}(2775, \cdot)\) n/a 844 2
6223.2.l \(\chi_{6223}(2285, \cdot)\) n/a 844 2
6223.2.q \(\chi_{6223}(362, \cdot)\) n/a 844 2
6223.2.r \(\chi_{6223}(489, \cdot)\) n/a 848 2
6223.2.u \(\chi_{6223}(2290, \cdot)\) n/a 3564 6
6223.2.v \(\chi_{6223}(540, \cdot)\) n/a 2598 6
6223.2.w \(\chi_{6223}(890, \cdot)\) n/a 3528 6
6223.2.x \(\chi_{6223}(1786, \cdot)\) n/a 3564 6
6223.2.y \(\chi_{6223}(1401, \cdot)\) n/a 3564 6
6223.2.z \(\chi_{6223}(8, \cdot)\) n/a 3564 6
6223.2.ba \(\chi_{6223}(764, \cdot)\) n/a 3564 6
6223.2.bb \(\chi_{6223}(897, \cdot)\) n/a 3564 6
6223.2.bc \(\chi_{6223}(3705, \cdot)\) n/a 2538 6
6223.2.bd \(\chi_{6223}(226, \cdot)\) n/a 2538 6
6223.2.be \(\chi_{6223}(99, \cdot)\) n/a 2592 6
6223.2.bh \(\chi_{6223}(825, \cdot)\) n/a 3564 6
6223.2.bi \(\chi_{6223}(881, \cdot)\) n/a 2544 6
6223.2.bj \(\chi_{6223}(888, \cdot)\) n/a 3564 6
6223.2.bk \(\chi_{6223}(377, \cdot)\) n/a 3564 6
6223.2.bl \(\chi_{6223}(1014, \cdot)\) n/a 3564 6
6223.2.bm \(\chi_{6223}(2127, \cdot)\) n/a 3564 6
6223.2.bz \(\chi_{6223}(349, \cdot)\) n/a 3564 6
6223.2.ca \(\chi_{6223}(111, \cdot)\) n/a 3564 6
6223.2.cf \(\chi_{6223}(313, \cdot)\) n/a 2538 6
6223.2.ci \(\chi_{6223}(2726, \cdot)\) n/a 2538 6
6223.2.cj \(\chi_{6223}(440, \cdot)\) n/a 2532 6
6223.2.cm \(\chi_{6223}(221, \cdot)\) n/a 7152 12
6223.2.cn \(\chi_{6223}(1810, \cdot)\) n/a 7152 12
6223.2.co \(\chi_{6223}(25, \cdot)\) n/a 7152 12
6223.2.cp \(\chi_{6223}(708, \cdot)\) n/a 7128 12
6223.2.cq \(\chi_{6223}(533, \cdot)\) n/a 7128 12
6223.2.cr \(\chi_{6223}(400, \cdot)\) n/a 7128 12
6223.2.cs \(\chi_{6223}(330, \cdot)\) n/a 7128 12
6223.2.ct \(\chi_{6223}(50, \cdot)\) n/a 5196 12
6223.2.cu \(\chi_{6223}(1751, \cdot)\) n/a 7128 12
6223.2.cv \(\chi_{6223}(673, \cdot)\) n/a 7128 12
6223.2.cw \(\chi_{6223}(270, \cdot)\) n/a 7152 12
6223.2.cx \(\chi_{6223}(200, \cdot)\) n/a 7152 12
6223.2.cy \(\chi_{6223}(823, \cdot)\) n/a 7152 12
6223.2.cz \(\chi_{6223}(249, \cdot)\) n/a 7152 12
6223.2.da \(\chi_{6223}(100, \cdot)\) n/a 7152 12
6223.2.db \(\chi_{6223}(527, \cdot)\) n/a 7152 12
6223.2.dc \(\chi_{6223}(800, \cdot)\) n/a 7152 12
6223.2.dd \(\chi_{6223}(177, \cdot)\) n/a 5064 12
6223.2.de \(\chi_{6223}(2, \cdot)\) n/a 7152 12
6223.2.df \(\chi_{6223}(431, \cdot)\) n/a 7152 12
6223.2.dg \(\chi_{6223}(1054, \cdot)\) n/a 7152 12
6223.2.dh \(\chi_{6223}(1159, \cdot)\) n/a 7152 12
6223.2.di \(\chi_{6223}(382, \cdot)\) n/a 7056 12
6223.2.dj \(\chi_{6223}(135, \cdot)\) n/a 7152 12
6223.2.dk \(\chi_{6223}(667, \cdot)\) n/a 5064 12
6223.2.dl \(\chi_{6223}(354, \cdot)\) n/a 7152 12
6223.2.dm \(\chi_{6223}(849, \cdot)\) n/a 7152 12
6223.2.dn \(\chi_{6223}(165, \cdot)\) n/a 5064 12
6223.2.do \(\chi_{6223}(107, \cdot)\) n/a 7152 12
6223.2.dp \(\chi_{6223}(891, \cdot)\) n/a 7152 12
6223.2.dq \(\chi_{6223}(1768, \cdot)\) n/a 7152 12
6223.2.dr \(\chi_{6223}(1219, \cdot)\) n/a 7128 12
6223.2.ds \(\chi_{6223}(640, \cdot)\) n/a 7152 12
6223.2.dx \(\chi_{6223}(633, \cdot)\) n/a 7152 12
6223.2.dy \(\chi_{6223}(5, \cdot)\) n/a 7152 12
6223.2.eb \(\chi_{6223}(160, \cdot)\) n/a 7128 12
6223.2.eo \(\chi_{6223}(27, \cdot)\) n/a 7128 12
6223.2.ep \(\chi_{6223}(20, \cdot)\) n/a 7128 12
6223.2.eq \(\chi_{6223}(132, \cdot)\) n/a 7128 12
6223.2.er \(\chi_{6223}(391, \cdot)\) n/a 5088 12
6223.2.es \(\chi_{6223}(1280, \cdot)\) n/a 7128 12
6223.2.et \(\chi_{6223}(181, \cdot)\) n/a 7128 12
6223.2.ey \(\chi_{6223}(250, \cdot)\) n/a 7152 12
6223.2.ez \(\chi_{6223}(1153, \cdot)\) n/a 7152 12
6223.2.fa \(\chi_{6223}(675, \cdot)\) n/a 7152 12
6223.2.fb \(\chi_{6223}(89, \cdot)\) n/a 7152 12
6223.2.fc \(\chi_{6223}(10, \cdot)\) n/a 7152 12
6223.2.fd \(\chi_{6223}(528, \cdot)\) n/a 7152 12
6223.2.fe \(\chi_{6223}(54, \cdot)\) n/a 7152 12
6223.2.ff \(\chi_{6223}(80, \cdot)\) n/a 5064 12
6223.2.ge \(\chi_{6223}(2917, \cdot)\) n/a 7152 12
6223.2.gf \(\chi_{6223}(724, \cdot)\) n/a 7152 12
6223.2.gg \(\chi_{6223}(33, \cdot)\) n/a 7152 12
6223.2.gh \(\chi_{6223}(887, \cdot)\) n/a 7152 12
6223.2.gi \(\chi_{6223}(507, \cdot)\) n/a 7152 12
6223.2.gj \(\chi_{6223}(444, \cdot)\) n/a 7152 12
6223.2.gk \(\chi_{6223}(619, \cdot)\) n/a 5064 12
6223.2.gl \(\chi_{6223}(334, \cdot)\) n/a 7152 12
6223.2.gm \(\chi_{6223}(320, \cdot)\) n/a 7152 12
6223.2.gn \(\chi_{6223}(178, \cdot)\) n/a 5064 12
6223.2.go \(\chi_{6223}(108, \cdot)\) n/a 7152 12
6223.2.gp \(\chi_{6223}(222, \cdot)\) n/a 7152 12
6223.2.hg \(\chi_{6223}(955, \cdot)\) n/a 7152 12
6223.2.hj \(\chi_{6223}(1021, \cdot)\) n/a 7128 12
6223.2.hk \(\chi_{6223}(88, \cdot)\) n/a 21420 36
6223.2.hl \(\chi_{6223}(60, \cdot)\) n/a 21420 36
6223.2.hm \(\chi_{6223}(113, \cdot)\) n/a 21456 36
6223.2.hn \(\chi_{6223}(15, \cdot)\) n/a 21456 36
6223.2.ho \(\chi_{6223}(148, \cdot)\) n/a 15552 36
6223.2.hp \(\chi_{6223}(36, \cdot)\) n/a 21456 36
6223.2.hq \(\chi_{6223}(176, \cdot)\) n/a 21456 36
6223.2.hr \(\chi_{6223}(22, \cdot)\) n/a 21456 36
6223.2.hs \(\chi_{6223}(120, \cdot)\) n/a 21456 36
6223.2.ht \(\chi_{6223}(375, \cdot)\) n/a 21420 36
6223.2.hu \(\chi_{6223}(247, \cdot)\) n/a 21420 36
6223.2.hv \(\chi_{6223}(18, \cdot)\) n/a 15228 36
6223.2.hw \(\chi_{6223}(142, \cdot)\) n/a 21420 36
6223.2.hx \(\chi_{6223}(291, \cdot)\) n/a 21420 36
6223.2.hy \(\chi_{6223}(11, \cdot)\) n/a 21420 36
6223.2.hz \(\chi_{6223}(240, \cdot)\) n/a 21420 36
6223.2.ia \(\chi_{6223}(275, \cdot)\) n/a 15228 36
6223.2.ib \(\chi_{6223}(296, \cdot)\) n/a 21420 36
6223.2.ic \(\chi_{6223}(72, \cdot)\) n/a 21420 36
6223.2.id \(\chi_{6223}(37, \cdot)\) n/a 21420 36
6223.2.ie \(\chi_{6223}(9, \cdot)\) n/a 21420 36
6223.2.if \(\chi_{6223}(44, \cdot)\) n/a 21420 36
6223.2.ig \(\chi_{6223}(198, \cdot)\) n/a 21420 36
6223.2.ih \(\chi_{6223}(71, \cdot)\) n/a 21456 36
6223.2.ii \(\chi_{6223}(12, \cdot)\) n/a 21420 36
6223.2.il \(\chi_{6223}(437, \cdot)\) n/a 21420 36
6223.2.io \(\chi_{6223}(55, \cdot)\) n/a 21456 36
6223.2.jb \(\chi_{6223}(531, \cdot)\) n/a 21456 36
6223.2.jc \(\chi_{6223}(48, \cdot)\) n/a 15192 36
6223.2.jd \(\chi_{6223}(6, \cdot)\) n/a 21456 36
6223.2.je \(\chi_{6223}(90, \cdot)\) n/a 21456 36
6223.2.jf \(\chi_{6223}(83, \cdot)\) n/a 21456 36
6223.2.jg \(\chi_{6223}(139, \cdot)\) n/a 21456 36
6223.2.jl \(\chi_{6223}(110, \cdot)\) n/a 21420 36
6223.2.jm \(\chi_{6223}(185, \cdot)\) n/a 21420 36
6223.2.jn \(\chi_{6223}(472, \cdot)\) n/a 15228 36
6223.2.jo \(\chi_{6223}(45, \cdot)\) n/a 21420 36
6223.2.jp \(\chi_{6223}(96, \cdot)\) n/a 21420 36
6223.2.jq \(\chi_{6223}(59, \cdot)\) n/a 21420 36
6223.2.jr \(\chi_{6223}(297, \cdot)\) n/a 21420 36
6223.2.ke \(\chi_{6223}(166, \cdot)\) n/a 15228 36
6223.2.kf \(\chi_{6223}(493, \cdot)\) n/a 21420 36
6223.2.kg \(\chi_{6223}(24, \cdot)\) n/a 21420 36
6223.2.kh \(\chi_{6223}(3, \cdot)\) n/a 21420 36
6223.2.ki \(\chi_{6223}(101, \cdot)\) n/a 21420 36
6223.2.kj \(\chi_{6223}(150, \cdot)\) n/a 21420 36
6223.2.ky \(\chi_{6223}(173, \cdot)\) n/a 21420 36
6223.2.lb \(\chi_{6223}(237, \cdot)\) n/a 21456 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6223))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6223)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(127))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(889))\)\(^{\oplus 2}\)