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Properties

Label 4275.2
Level 4275
Weight 2
Dimension 467052
Nonzero newspaces 96
Sturm bound 2592000

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Defining parameters

Level: \( N \) = \( 4275 = 3^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(2592000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4275))\).

Total New Old
Modular forms 656064 473324 182740
Cusp forms 639937 467052 172885
Eisenstein series 16127 6272 9855

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4275))\)

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
4275.2.a \(\chi_{4275}(1, \cdot)\) 4275.2.a.a 1 1
4275.2.a.b 1
4275.2.a.c 1
4275.2.a.d 1
4275.2.a.e 1
4275.2.a.f 1
4275.2.a.g 1
4275.2.a.h 1
4275.2.a.i 1
4275.2.a.j 1
4275.2.a.k 1
4275.2.a.l 1
4275.2.a.m 1
4275.2.a.n 1
4275.2.a.o 1
4275.2.a.p 1
4275.2.a.q 1
4275.2.a.r 2
4275.2.a.s 2
4275.2.a.t 2
4275.2.a.u 2
4275.2.a.v 2
4275.2.a.w 2
4275.2.a.x 2
4275.2.a.y 2
4275.2.a.z 3
4275.2.a.ba 3
4275.2.a.bb 3
4275.2.a.bc 3
4275.2.a.bd 3
4275.2.a.be 3
4275.2.a.bf 3
4275.2.a.bg 3
4275.2.a.bh 3
4275.2.a.bi 3
4275.2.a.bj 3
4275.2.a.bk 3
4275.2.a.bl 3
4275.2.a.bm 3
4275.2.a.bn 3
4275.2.a.bo 4
4275.2.a.bp 4
4275.2.a.bq 6
4275.2.a.br 6
4275.2.a.bs 6
4275.2.a.bt 6
4275.2.a.bu 6
4275.2.a.bv 7
4275.2.a.bw 7
4275.2.a.bx 12
4275.2.b \(\chi_{4275}(4274, \cdot)\) n/a 120 1
4275.2.c \(\chi_{4275}(2224, \cdot)\) n/a 136 1
4275.2.h \(\chi_{4275}(2051, \cdot)\) n/a 128 1
4275.2.i \(\chi_{4275}(1426, \cdot)\) n/a 684 2
4275.2.j \(\chi_{4275}(976, \cdot)\) n/a 748 2
4275.2.k \(\chi_{4275}(676, \cdot)\) n/a 312 2
4275.2.l \(\chi_{4275}(2101, \cdot)\) n/a 748 2
4275.2.n \(\chi_{4275}(818, \cdot)\) n/a 216 2
4275.2.p \(\chi_{4275}(1918, \cdot)\) n/a 296 2
4275.2.q \(\chi_{4275}(856, \cdot)\) n/a 904 4
4275.2.t \(\chi_{4275}(49, \cdot)\) n/a 712 2
4275.2.u \(\chi_{4275}(1874, \cdot)\) n/a 712 2
4275.2.x \(\chi_{4275}(626, \cdot)\) n/a 748 2
4275.2.y \(\chi_{4275}(1076, \cdot)\) n/a 748 2
4275.2.bd \(\chi_{4275}(1376, \cdot)\) n/a 256 2
4275.2.be \(\chi_{4275}(449, \cdot)\) n/a 240 2
4275.2.bf \(\chi_{4275}(1774, \cdot)\) n/a 296 2
4275.2.bk \(\chi_{4275}(799, \cdot)\) n/a 648 2
4275.2.bl \(\chi_{4275}(1474, \cdot)\) n/a 712 2
4275.2.bm \(\chi_{4275}(1424, \cdot)\) n/a 712 2
4275.2.bn \(\chi_{4275}(749, \cdot)\) n/a 712 2
4275.2.bq \(\chi_{4275}(3926, \cdot)\) n/a 748 2
4275.2.bt \(\chi_{4275}(226, \cdot)\) n/a 930 6
4275.2.bu \(\chi_{4275}(301, \cdot)\) n/a 2244 6
4275.2.bv \(\chi_{4275}(1201, \cdot)\) n/a 2244 6
4275.2.by \(\chi_{4275}(341, \cdot)\) n/a 800 4
4275.2.bz \(\chi_{4275}(514, \cdot)\) n/a 896 4
4275.2.ca \(\chi_{4275}(854, \cdot)\) n/a 800 4
4275.2.cd \(\chi_{4275}(943, \cdot)\) n/a 1424 4
4275.2.cf \(\chi_{4275}(68, \cdot)\) n/a 1424 4
4275.2.ch \(\chi_{4275}(368, \cdot)\) n/a 480 4
4275.2.ck \(\chi_{4275}(493, \cdot)\) n/a 1424 4
4275.2.cm \(\chi_{4275}(1057, \cdot)\) n/a 1424 4
4275.2.co \(\chi_{4275}(932, \cdot)\) n/a 1296 4
4275.2.cq \(\chi_{4275}(182, \cdot)\) n/a 1424 4
4275.2.cr \(\chi_{4275}(1243, \cdot)\) n/a 592 4
4275.2.ct \(\chi_{4275}(391, \cdot)\) n/a 4768 8
4275.2.cu \(\chi_{4275}(106, \cdot)\) n/a 4768 8
4275.2.cv \(\chi_{4275}(286, \cdot)\) n/a 4320 8
4275.2.cw \(\chi_{4275}(406, \cdot)\) n/a 1984 8
4275.2.cz \(\chi_{4275}(1024, \cdot)\) n/a 2136 6
4275.2.da \(\chi_{4275}(299, \cdot)\) n/a 2136 6
4275.2.db \(\chi_{4275}(401, \cdot)\) n/a 2244 6
4275.2.dc \(\chi_{4275}(926, \cdot)\) n/a 756 6
4275.2.dl \(\chi_{4275}(1649, \cdot)\) n/a 2136 6
4275.2.dm \(\chi_{4275}(199, \cdot)\) n/a 888 6
4275.2.dn \(\chi_{4275}(224, \cdot)\) n/a 720 6
4275.2.do \(\chi_{4275}(499, \cdot)\) n/a 2136 6
4275.2.dp \(\chi_{4275}(326, \cdot)\) n/a 2244 6
4275.2.ds \(\chi_{4275}(37, \cdot)\) n/a 1984 8
4275.2.du \(\chi_{4275}(647, \cdot)\) n/a 1440 8
4275.2.dw \(\chi_{4275}(506, \cdot)\) n/a 4768 8
4275.2.dz \(\chi_{4275}(64, \cdot)\) n/a 1984 8
4275.2.ea \(\chi_{4275}(179, \cdot)\) n/a 1600 8
4275.2.ef \(\chi_{4275}(734, \cdot)\) n/a 4768 8
4275.2.eg \(\chi_{4275}(284, \cdot)\) n/a 4768 8
4275.2.eh \(\chi_{4275}(619, \cdot)\) n/a 4768 8
4275.2.ei \(\chi_{4275}(229, \cdot)\) n/a 4320 8
4275.2.en \(\chi_{4275}(221, \cdot)\) n/a 4768 8
4275.2.eo \(\chi_{4275}(56, \cdot)\) n/a 4768 8
4275.2.et \(\chi_{4275}(521, \cdot)\) n/a 1600 8
4275.2.ew \(\chi_{4275}(164, \cdot)\) n/a 4768 8
4275.2.ex \(\chi_{4275}(904, \cdot)\) n/a 4768 8
4275.2.ez \(\chi_{4275}(218, \cdot)\) n/a 4272 12
4275.2.fc \(\chi_{4275}(268, \cdot)\) n/a 4272 12
4275.2.fd \(\chi_{4275}(307, \cdot)\) n/a 1776 12
4275.2.fe \(\chi_{4275}(632, \cdot)\) n/a 4272 12
4275.2.ff \(\chi_{4275}(332, \cdot)\) n/a 1440 12
4275.2.fi \(\chi_{4275}(193, \cdot)\) n/a 4272 12
4275.2.fk \(\chi_{4275}(61, \cdot)\) n/a 14304 24
4275.2.fl \(\chi_{4275}(271, \cdot)\) n/a 5952 24
4275.2.fm \(\chi_{4275}(16, \cdot)\) n/a 14304 24
4275.2.fo \(\chi_{4275}(217, \cdot)\) n/a 3968 16
4275.2.fp \(\chi_{4275}(353, \cdot)\) n/a 9536 16
4275.2.fr \(\chi_{4275}(77, \cdot)\) n/a 8640 16
4275.2.ft \(\chi_{4275}(202, \cdot)\) n/a 9536 16
4275.2.fv \(\chi_{4275}(322, \cdot)\) n/a 9536 16
4275.2.fy \(\chi_{4275}(197, \cdot)\) n/a 3200 16
4275.2.ga \(\chi_{4275}(83, \cdot)\) n/a 9536 16
4275.2.gc \(\chi_{4275}(88, \cdot)\) n/a 9536 16
4275.2.gd \(\chi_{4275}(344, \cdot)\) n/a 14304 24
4275.2.ge \(\chi_{4275}(4, \cdot)\) n/a 14304 24
4275.2.gl \(\chi_{4275}(71, \cdot)\) n/a 4800 24
4275.2.gm \(\chi_{4275}(41, \cdot)\) n/a 14304 24
4275.2.gn \(\chi_{4275}(454, \cdot)\) n/a 14304 24
4275.2.go \(\chi_{4275}(89, \cdot)\) n/a 4800 24
4275.2.gp \(\chi_{4275}(244, \cdot)\) n/a 5952 24
4275.2.gq \(\chi_{4275}(14, \cdot)\) n/a 14304 24
4275.2.gx \(\chi_{4275}(86, \cdot)\) n/a 14304 24
4275.2.gz \(\chi_{4275}(22, \cdot)\) n/a 28608 48
4275.2.hc \(\chi_{4275}(23, \cdot)\) n/a 28608 48
4275.2.hd \(\chi_{4275}(17, \cdot)\) n/a 9600 48
4275.2.he \(\chi_{4275}(13, \cdot)\) n/a 28608 48
4275.2.hf \(\chi_{4275}(127, \cdot)\) n/a 11904 48
4275.2.hi \(\chi_{4275}(47, \cdot)\) n/a 28608 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4275)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4275))\)\(^{\oplus 1}\)