Properties

Label 4284.2
Level 4284
Weight 2
Dimension 217372
Nonzero newspaces 100
Sturm bound 1990656

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Defining parameters

Level: \( N \) = \( 4284 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(1990656\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4284))\).

Total New Old
Modular forms 505344 220068 285276
Cusp forms 489985 217372 272613
Eisenstein series 15359 2696 12663

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4284))\)

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
4284.2.a \(\chi_{4284}(1, \cdot)\) 4284.2.a.a 1 1
4284.2.a.b 1
4284.2.a.c 1
4284.2.a.d 1
4284.2.a.e 1
4284.2.a.f 1
4284.2.a.g 1
4284.2.a.h 1
4284.2.a.i 1
4284.2.a.j 2
4284.2.a.k 2
4284.2.a.l 2
4284.2.a.m 2
4284.2.a.n 2
4284.2.a.o 2
4284.2.a.p 2
4284.2.a.q 2
4284.2.a.r 3
4284.2.a.s 3
4284.2.a.t 3
4284.2.a.u 3
4284.2.a.v 3
4284.2.c \(\chi_{4284}(307, \cdot)\) n/a 320 1
4284.2.d \(\chi_{4284}(3025, \cdot)\) 4284.2.d.a 2 1
4284.2.d.b 2
4284.2.d.c 2
4284.2.d.d 6
4284.2.d.e 8
4284.2.d.f 12
4284.2.d.g 12
4284.2.g \(\chi_{4284}(2141, \cdot)\) 4284.2.g.a 48 1
4284.2.h \(\chi_{4284}(3095, \cdot)\) n/a 192 1
4284.2.j \(\chi_{4284}(3401, \cdot)\) 4284.2.j.a 20 1
4284.2.j.b 20
4284.2.m \(\chi_{4284}(1835, \cdot)\) n/a 216 1
4284.2.n \(\chi_{4284}(3331, \cdot)\) n/a 356 1
4284.2.q \(\chi_{4284}(1633, \cdot)\) n/a 256 2
4284.2.r \(\chi_{4284}(1429, \cdot)\) n/a 192 2
4284.2.s \(\chi_{4284}(613, \cdot)\) n/a 108 2
4284.2.t \(\chi_{4284}(205, \cdot)\) n/a 256 2
4284.2.v \(\chi_{4284}(55, \cdot)\) n/a 712 2
4284.2.x \(\chi_{4284}(2393, \cdot)\) 4284.2.x.a 96 2
4284.2.z \(\chi_{4284}(3277, \cdot)\) 4284.2.z.a 4 2
4284.2.z.b 16
4284.2.z.c 16
4284.2.z.d 20
4284.2.z.e 32
4284.2.bb \(\chi_{4284}(2087, \cdot)\) n/a 432 2
4284.2.bd \(\chi_{4284}(2209, \cdot)\) n/a 288 2
4284.2.be \(\chi_{4284}(2551, \cdot)\) n/a 1536 2
4284.2.bh \(\chi_{4284}(443, \cdot)\) n/a 1536 2
4284.2.bi \(\chi_{4284}(1937, \cdot)\) n/a 288 2
4284.2.bl \(\chi_{4284}(271, \cdot)\) n/a 712 2
4284.2.bo \(\chi_{4284}(3127, \cdot)\) n/a 1712 2
4284.2.br \(\chi_{4284}(475, \cdot)\) n/a 1712 2
4284.2.bu \(\chi_{4284}(341, \cdot)\) 4284.2.bu.a 4 2
4284.2.bu.b 4
4284.2.bu.c 4
4284.2.bu.d 4
4284.2.bu.e 36
4284.2.bu.f 36
4284.2.bv \(\chi_{4284}(407, \cdot)\) n/a 1296 2
4284.2.by \(\chi_{4284}(1019, \cdot)\) n/a 1712 2
4284.2.ca \(\chi_{4284}(545, \cdot)\) n/a 256 2
4284.2.cb \(\chi_{4284}(1361, \cdot)\) n/a 256 2
4284.2.cd \(\chi_{4284}(611, \cdot)\) n/a 576 2
4284.2.cf \(\chi_{4284}(1529, \cdot)\) 4284.2.cf.a 96 2
4284.2.ci \(\chi_{4284}(239, \cdot)\) n/a 1152 2
4284.2.cj \(\chi_{4284}(2279, \cdot)\) n/a 1536 2
4284.2.cl \(\chi_{4284}(713, \cdot)\) n/a 288 2
4284.2.co \(\chi_{4284}(101, \cdot)\) n/a 288 2
4284.2.cq \(\chi_{4284}(1871, \cdot)\) n/a 512 2
4284.2.cr \(\chi_{4284}(1531, \cdot)\) n/a 640 2
4284.2.ct \(\chi_{4284}(373, \cdot)\) n/a 288 2
4284.2.cw \(\chi_{4284}(169, \cdot)\) n/a 216 2
4284.2.cy \(\chi_{4284}(103, \cdot)\) n/a 1536 2
4284.2.cz \(\chi_{4284}(1735, \cdot)\) n/a 1536 2
4284.2.dc \(\chi_{4284}(1801, \cdot)\) n/a 120 2
4284.2.dd \(\chi_{4284}(3467, \cdot)\) n/a 1712 2
4284.2.dg \(\chi_{4284}(3197, \cdot)\) n/a 256 2
4284.2.dj \(\chi_{4284}(1291, \cdot)\) n/a 1712 2
4284.2.dk \(\chi_{4284}(253, \cdot)\) n/a 184 4
4284.2.dl \(\chi_{4284}(1079, \cdot)\) n/a 864 4
4284.2.do \(\chi_{4284}(559, \cdot)\) n/a 1424 4
4284.2.dp \(\chi_{4284}(1385, \cdot)\) n/a 192 4
4284.2.ds \(\chi_{4284}(89, \cdot)\) n/a 192 4
4284.2.du \(\chi_{4284}(523, \cdot)\) n/a 1424 4
4284.2.dw \(\chi_{4284}(421, \cdot)\) n/a 432 4
4284.2.dy \(\chi_{4284}(191, \cdot)\) n/a 3424 4
4284.2.eb \(\chi_{4284}(1271, \cdot)\) n/a 3424 4
4284.2.ec \(\chi_{4284}(2461, \cdot)\) n/a 576 4
4284.2.ef \(\chi_{4284}(625, \cdot)\) n/a 576 4
4284.2.eg \(\chi_{4284}(659, \cdot)\) n/a 2592 4
4284.2.ei \(\chi_{4284}(727, \cdot)\) n/a 3424 4
4284.2.ek \(\chi_{4284}(2189, \cdot)\) n/a 576 4
4284.2.en \(\chi_{4284}(353, \cdot)\) n/a 576 4
4284.2.eo \(\chi_{4284}(1543, \cdot)\) n/a 3424 4
4284.2.er \(\chi_{4284}(115, \cdot)\) n/a 3424 4
4284.2.es \(\chi_{4284}(293, \cdot)\) n/a 576 4
4284.2.eu \(\chi_{4284}(863, \cdot)\) n/a 1152 4
4284.2.ew \(\chi_{4284}(361, \cdot)\) n/a 240 4
4284.2.fa \(\chi_{4284}(181, \cdot)\) n/a 480 8
4284.2.fb \(\chi_{4284}(197, \cdot)\) n/a 288 8
4284.2.fc \(\chi_{4284}(379, \cdot)\) n/a 2160 8
4284.2.fd \(\chi_{4284}(503, \cdot)\) n/a 2304 8
4284.2.fi \(\chi_{4284}(865, \cdot)\) n/a 480 8
4284.2.fj \(\chi_{4284}(179, \cdot)\) n/a 2304 8
4284.2.fk \(\chi_{4284}(355, \cdot)\) n/a 6848 8
4284.2.fl \(\chi_{4284}(257, \cdot)\) n/a 1152 8
4284.2.fq \(\chi_{4284}(535, \cdot)\) n/a 6848 8
4284.2.fr \(\chi_{4284}(223, \cdot)\) n/a 6848 8
4284.2.fs \(\chi_{4284}(461, \cdot)\) n/a 1152 8
4284.2.ft \(\chi_{4284}(185, \cdot)\) n/a 1152 8
4284.2.fw \(\chi_{4284}(25, \cdot)\) n/a 1152 8
4284.2.fx \(\chi_{4284}(263, \cdot)\) n/a 6848 8
4284.2.gc \(\chi_{4284}(841, \cdot)\) n/a 864 8
4284.2.gd \(\chi_{4284}(457, \cdot)\) n/a 1152 8
4284.2.ge \(\chi_{4284}(695, \cdot)\) n/a 6848 8
4284.2.gf \(\chi_{4284}(155, \cdot)\) n/a 5184 8
4284.2.gk \(\chi_{4284}(19, \cdot)\) n/a 2848 8
4284.2.gl \(\chi_{4284}(593, \cdot)\) n/a 384 8
4284.2.gm \(\chi_{4284}(401, \cdot)\) n/a 2304 16
4284.2.gn \(\chi_{4284}(241, \cdot)\) n/a 2304 16
4284.2.gq \(\chi_{4284}(79, \cdot)\) n/a 13696 16
4284.2.gr \(\chi_{4284}(299, \cdot)\) n/a 13696 16
4284.2.gw \(\chi_{4284}(143, \cdot)\) n/a 4608 16
4284.2.gx \(\chi_{4284}(167, \cdot)\) n/a 13696 16
4284.2.gy \(\chi_{4284}(163, \cdot)\) n/a 5696 16
4284.2.gz \(\chi_{4284}(211, \cdot)\) n/a 10368 16
4284.2.he \(\chi_{4284}(233, \cdot)\) n/a 768 16
4284.2.hf \(\chi_{4284}(29, \cdot)\) n/a 1728 16
4284.2.hg \(\chi_{4284}(73, \cdot)\) n/a 960 16
4284.2.hh \(\chi_{4284}(97, \cdot)\) n/a 2304 16
4284.2.hm \(\chi_{4284}(61, \cdot)\) n/a 2304 16
4284.2.hn \(\chi_{4284}(65, \cdot)\) n/a 2304 16
4284.2.hq \(\chi_{4284}(131, \cdot)\) n/a 13696 16
4284.2.hr \(\chi_{4284}(403, \cdot)\) n/a 13696 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4284))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4284)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(714))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1071))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1428))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2142))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4284))\)\(^{\oplus 1}\)