↑

Properties

Label 9675.2
Level 9675
Weight 2
Dimension 2416926
Nonzero newspaces 120
Sturm bound 13305600

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 9675 = 3^{2} \cdot 5^{2} \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(13305600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9675))\).

Total New Old
Modular forms 3345216 2432054 913162
Cusp forms 3307585 2416926 890659
Eisenstein series 37631 15128 22503

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9675))\)

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
9675.2.a \(\chi_{9675}(1, \cdot)\) 9675.2.a.a 1 1
9675.2.a.b 1
9675.2.a.c 1
9675.2.a.d 1
9675.2.a.e 1
9675.2.a.f 1
9675.2.a.g 1
9675.2.a.h 1
9675.2.a.i 1
9675.2.a.j 1
9675.2.a.k 1
9675.2.a.l 1
9675.2.a.m 1
9675.2.a.n 1
9675.2.a.o 1
9675.2.a.p 1
9675.2.a.q 1
9675.2.a.r 1
9675.2.a.s 1
9675.2.a.t 1
9675.2.a.u 1
9675.2.a.v 1
9675.2.a.w 1
9675.2.a.x 1
9675.2.a.y 2
9675.2.a.z 2
9675.2.a.ba 2
9675.2.a.bb 2
9675.2.a.bc 2
9675.2.a.bd 2
9675.2.a.be 2
9675.2.a.bf 2
9675.2.a.bg 2
9675.2.a.bh 2
9675.2.a.bi 2
9675.2.a.bj 2
9675.2.a.bk 2
9675.2.a.bl 2
9675.2.a.bm 2
9675.2.a.bn 2
9675.2.a.bo 3
9675.2.a.bp 3
9675.2.a.bq 3
9675.2.a.br 3
9675.2.a.bs 3
9675.2.a.bt 3
9675.2.a.bu 3
9675.2.a.bv 4
9675.2.a.bw 5
9675.2.a.bx 5
9675.2.a.by 5
9675.2.a.bz 5
9675.2.a.ca 5
9675.2.a.cb 5
9675.2.a.cc 5
9675.2.a.cd 5
9675.2.a.ce 5
9675.2.a.cf 5
9675.2.a.cg 5
9675.2.a.ch 5
9675.2.a.ci 5
9675.2.a.cj 6
9675.2.a.ck 6
9675.2.a.cl 6
9675.2.a.cm 7
9675.2.a.cn 7
9675.2.a.co 8
9675.2.a.cp 8
9675.2.a.cq 8
9675.2.a.cr 8
9675.2.a.cs 9
9675.2.a.ct 9
9675.2.a.cu 10
9675.2.a.cv 10
9675.2.a.cw 10
9675.2.a.cx 10
9675.2.a.cy 12
9675.2.a.cz 12
9675.2.a.da 20
9675.2.a.db 20
9675.2.b \(\chi_{9675}(1549, \cdot)\) n/a 316 1
9675.2.d \(\chi_{9675}(9674, \cdot)\) n/a 264 1
9675.2.g \(\chi_{9675}(8126, \cdot)\) n/a 280 1
9675.2.i \(\chi_{9675}(3226, \cdot)\) n/a 1596 2
9675.2.j \(\chi_{9675}(2401, \cdot)\) n/a 1660 2
9675.2.k \(\chi_{9675}(1726, \cdot)\) n/a 1660 2
9675.2.l \(\chi_{9675}(4951, \cdot)\) n/a 690 2
9675.2.m \(\chi_{9675}(818, \cdot)\) n/a 504 2
9675.2.p \(\chi_{9675}(343, \cdot)\) n/a 656 2
9675.2.q \(\chi_{9675}(1936, \cdot)\) n/a 2104 4
9675.2.s \(\chi_{9675}(4049, \cdot)\) n/a 528 2
9675.2.u \(\chi_{9675}(6499, \cdot)\) n/a 656 2
9675.2.v \(\chi_{9675}(6401, \cdot)\) n/a 1660 2
9675.2.ba \(\chi_{9675}(1676, \cdot)\) n/a 1660 2
9675.2.bc \(\chi_{9675}(5726, \cdot)\) n/a 1660 2
9675.2.bf \(\chi_{9675}(724, \cdot)\) n/a 1576 2
9675.2.bg \(\chi_{9675}(1499, \cdot)\) n/a 1576 2
9675.2.bi \(\chi_{9675}(3224, \cdot)\) n/a 1576 2
9675.2.bk \(\chi_{9675}(49, \cdot)\) n/a 1576 2
9675.2.bm \(\chi_{9675}(4774, \cdot)\) n/a 1512 2
9675.2.bp \(\chi_{9675}(824, \cdot)\) n/a 1576 2
9675.2.br \(\chi_{9675}(2501, \cdot)\) n/a 556 2
9675.2.bt \(\chi_{9675}(226, \cdot)\) n/a 2076 6
9675.2.bu \(\chi_{9675}(386, \cdot)\) n/a 1760 4
9675.2.by \(\chi_{9675}(3484, \cdot)\) n/a 2096 4
9675.2.ca \(\chi_{9675}(1934, \cdot)\) n/a 1760 4
9675.2.cc \(\chi_{9675}(4607, \cdot)\) n/a 1056 4
9675.2.cd \(\chi_{9675}(3232, \cdot)\) n/a 1312 4
9675.2.cf \(\chi_{9675}(7, \cdot)\) n/a 3152 4
9675.2.ci \(\chi_{9675}(682, \cdot)\) n/a 3152 4
9675.2.ck \(\chi_{9675}(2407, \cdot)\) n/a 3152 4
9675.2.cl \(\chi_{9675}(2882, \cdot)\) n/a 3024 4
9675.2.cn \(\chi_{9675}(2057, \cdot)\) n/a 3152 4
9675.2.cq \(\chi_{9675}(1382, \cdot)\) n/a 3152 4
9675.2.cr \(\chi_{9675}(2951, \cdot)\) n/a 1680 6
9675.2.cv \(\chi_{9675}(649, \cdot)\) n/a 1968 6
9675.2.cx \(\chi_{9675}(899, \cdot)\) n/a 1584 6
9675.2.cy \(\chi_{9675}(1081, \cdot)\) n/a 4384 8
9675.2.cz \(\chi_{9675}(436, \cdot)\) n/a 10528 8
9675.2.da \(\chi_{9675}(646, \cdot)\) n/a 10080 8
9675.2.db \(\chi_{9675}(1111, \cdot)\) n/a 10528 8
9675.2.dc \(\chi_{9675}(1117, \cdot)\) n/a 4384 8
9675.2.df \(\chi_{9675}(1592, \cdot)\) n/a 3360 8
9675.2.dg \(\chi_{9675}(676, \cdot)\) n/a 4140 12
9675.2.dh \(\chi_{9675}(526, \cdot)\) n/a 9960 12
9675.2.di \(\chi_{9675}(1951, \cdot)\) n/a 9960 12
9675.2.dj \(\chi_{9675}(1651, \cdot)\) n/a 9960 12
9675.2.dk \(\chi_{9675}(82, \cdot)\) n/a 3936 12
9675.2.dn \(\chi_{9675}(107, \cdot)\) n/a 3168 12
9675.2.dq \(\chi_{9675}(566, \cdot)\) n/a 3520 8
9675.2.dr \(\chi_{9675}(1339, \cdot)\) n/a 10528 8
9675.2.du \(\chi_{9675}(644, \cdot)\) n/a 10528 8
9675.2.dw \(\chi_{9675}(1469, \cdot)\) n/a 10528 8
9675.2.dy \(\chi_{9675}(259, \cdot)\) n/a 10080 8
9675.2.ea \(\chi_{9675}(79, \cdot)\) n/a 10528 8
9675.2.eb \(\chi_{9675}(209, \cdot)\) n/a 10528 8
9675.2.ee \(\chi_{9675}(596, \cdot)\) n/a 10528 8
9675.2.eh \(\chi_{9675}(1856, \cdot)\) n/a 10528 8
9675.2.ej \(\chi_{9675}(1031, \cdot)\) n/a 10528 8
9675.2.em \(\chi_{9675}(179, \cdot)\) n/a 3520 8
9675.2.eo \(\chi_{9675}(694, \cdot)\) n/a 4384 8
9675.2.eq \(\chi_{9675}(766, \cdot)\) n/a 13152 24
9675.2.et \(\chi_{9675}(26, \cdot)\) n/a 3336 12
9675.2.eu \(\chi_{9675}(124, \cdot)\) n/a 9456 12
9675.2.ex \(\chi_{9675}(524, \cdot)\) n/a 9456 12
9675.2.ez \(\chi_{9675}(149, \cdot)\) n/a 9456 12
9675.2.fb \(\chi_{9675}(274, \cdot)\) n/a 9456 12
9675.2.fd \(\chi_{9675}(574, \cdot)\) n/a 9456 12
9675.2.fe \(\chi_{9675}(374, \cdot)\) n/a 9456 12
9675.2.fh \(\chi_{9675}(851, \cdot)\) n/a 9960 12
9675.2.fk \(\chi_{9675}(2351, \cdot)\) n/a 9960 12
9675.2.fm \(\chi_{9675}(776, \cdot)\) n/a 9960 12
9675.2.fp \(\chi_{9675}(449, \cdot)\) n/a 3168 12
9675.2.fr \(\chi_{9675}(874, \cdot)\) n/a 3936 12
9675.2.ft \(\chi_{9675}(608, \cdot)\) n/a 21056 16
9675.2.fw \(\chi_{9675}(92, \cdot)\) n/a 21056 16
9675.2.fy \(\chi_{9675}(173, \cdot)\) n/a 20160 16
9675.2.fz \(\chi_{9675}(472, \cdot)\) n/a 21056 16
9675.2.gb \(\chi_{9675}(652, \cdot)\) n/a 21056 16
9675.2.ge \(\chi_{9675}(553, \cdot)\) n/a 21056 16
9675.2.gg \(\chi_{9675}(37, \cdot)\) n/a 8768 16
9675.2.gh \(\chi_{9675}(638, \cdot)\) n/a 7040 16
9675.2.gj \(\chi_{9675}(64, \cdot)\) n/a 13152 24
9675.2.gl \(\chi_{9675}(629, \cdot)\) n/a 10560 24
9675.2.go \(\chi_{9675}(161, \cdot)\) n/a 10560 24
9675.2.gq \(\chi_{9675}(443, \cdot)\) n/a 18912 24
9675.2.gt \(\chi_{9675}(68, \cdot)\) n/a 18912 24
9675.2.gv \(\chi_{9675}(293, \cdot)\) n/a 18912 24
9675.2.gw \(\chi_{9675}(457, \cdot)\) n/a 18912 24
9675.2.gy \(\chi_{9675}(157, \cdot)\) n/a 18912 24
9675.2.hb \(\chi_{9675}(607, \cdot)\) n/a 18912 24
9675.2.hd \(\chi_{9675}(757, \cdot)\) n/a 7872 24
9675.2.he \(\chi_{9675}(143, \cdot)\) n/a 6336 24
9675.2.hg \(\chi_{9675}(16, \cdot)\) n/a 63168 48
9675.2.hh \(\chi_{9675}(31, \cdot)\) n/a 63168 48
9675.2.hi \(\chi_{9675}(196, \cdot)\) n/a 63168 48
9675.2.hj \(\chi_{9675}(181, \cdot)\) n/a 26304 48
9675.2.hk \(\chi_{9675}(188, \cdot)\) n/a 21120 48
9675.2.hn \(\chi_{9675}(217, \cdot)\) n/a 26304 48
9675.2.hp \(\chi_{9675}(89, \cdot)\) n/a 21120 48
9675.2.hr \(\chi_{9675}(109, \cdot)\) n/a 26304 48
9675.2.hs \(\chi_{9675}(191, \cdot)\) n/a 63168 48
9675.2.hx \(\chi_{9675}(131, \cdot)\) n/a 63168 48
9675.2.hz \(\chi_{9675}(356, \cdot)\) n/a 63168 48
9675.2.ic \(\chi_{9675}(169, \cdot)\) n/a 63168 48
9675.2.id \(\chi_{9675}(29, \cdot)\) n/a 63168 48
9675.2.if \(\chi_{9675}(194, \cdot)\) n/a 63168 48
9675.2.ih \(\chi_{9675}(139, \cdot)\) n/a 63168 48
9675.2.ij \(\chi_{9675}(4, \cdot)\) n/a 63168 48
9675.2.im \(\chi_{9675}(104, \cdot)\) n/a 63168 48
9675.2.io \(\chi_{9675}(71, \cdot)\) n/a 21120 48
9675.2.ir \(\chi_{9675}(17, \cdot)\) n/a 42240 96
9675.2.is \(\chi_{9675}(28, \cdot)\) n/a 52608 96
9675.2.iu \(\chi_{9675}(148, \cdot)\) n/a 126336 96
9675.2.ix \(\chi_{9675}(112, \cdot)\) n/a 126336 96
9675.2.iz \(\chi_{9675}(22, \cdot)\) n/a 126336 96
9675.2.ja \(\chi_{9675}(47, \cdot)\) n/a 126336 96
9675.2.jc \(\chi_{9675}(38, \cdot)\) n/a 126336 96
9675.2.jf \(\chi_{9675}(23, \cdot)\) n/a 126336 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9675))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9675)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(387))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(645))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1075))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1935))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3225))\)\(^{\oplus 2}\)