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Properties

Label 9660.2
Level 9660
Weight 2
Dimension 929032
Nonzero newspaces 96
Sturm bound 9732096

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Defining parameters

Level: \( N \) = \( 9660 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(9732096\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9660))\).

Total New Old
Modular forms 2454144 934056 1520088
Cusp forms 2411905 929032 1482873
Eisenstein series 42239 5024 37215

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9660))\)

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
9660.2.a \(\chi_{9660}(1, \cdot)\) 9660.2.a.a 1 1
9660.2.a.b 1
9660.2.a.c 1
9660.2.a.d 1
9660.2.a.e 1
9660.2.a.f 1
9660.2.a.g 2
9660.2.a.h 2
9660.2.a.i 2
9660.2.a.j 2
9660.2.a.k 2
9660.2.a.l 2
9660.2.a.m 2
9660.2.a.n 3
9660.2.a.o 3
9660.2.a.p 3
9660.2.a.q 4
9660.2.a.r 5
9660.2.a.s 5
9660.2.a.t 5
9660.2.a.u 6
9660.2.a.v 6
9660.2.a.w 6
9660.2.a.x 7
9660.2.a.y 7
9660.2.a.z 8
9660.2.b \(\chi_{9660}(1931, \cdot)\) n/a 1536 1
9660.2.e \(\chi_{9660}(2071, \cdot)\) n/a 704 1
9660.2.f \(\chi_{9660}(461, \cdot)\) n/a 232 1
9660.2.i \(\chi_{9660}(3541, \cdot)\) n/a 128 1
9660.2.j \(\chi_{9660}(8189, \cdot)\) n/a 352 1
9660.2.m \(\chi_{9660}(1609, \cdot)\) n/a 192 1
9660.2.n \(\chi_{9660}(9659, \cdot)\) n/a 2288 1
9660.2.q \(\chi_{9660}(139, \cdot)\) n/a 1056 1
9660.2.r \(\chi_{9660}(7589, \cdot)\) n/a 288 1
9660.2.u \(\chi_{9660}(7729, \cdot)\) n/a 136 1
9660.2.v \(\chi_{9660}(6119, \cdot)\) n/a 1584 1
9660.2.y \(\chi_{9660}(9199, \cdot)\) n/a 864 1
9660.2.z \(\chi_{9660}(8051, \cdot)\) n/a 1056 1
9660.2.bc \(\chi_{9660}(1471, \cdot)\) n/a 576 1
9660.2.bd \(\chi_{9660}(9521, \cdot)\) n/a 192 1
9660.2.bg \(\chi_{9660}(1381, \cdot)\) n/a 232 2
9660.2.bj \(\chi_{9660}(827, \cdot)\) n/a 3456 2
9660.2.bk \(\chi_{9660}(5153, \cdot)\) n/a 528 2
9660.2.bl \(\chi_{9660}(967, \cdot)\) n/a 1584 2
9660.2.bm \(\chi_{9660}(2437, \cdot)\) n/a 288 2
9660.2.br \(\chi_{9660}(2897, \cdot)\) n/a 768 2
9660.2.bs \(\chi_{9660}(1427, \cdot)\) n/a 4224 2
9660.2.bt \(\chi_{9660}(3037, \cdot)\) n/a 352 2
9660.2.bu \(\chi_{9660}(643, \cdot)\) n/a 2304 2
9660.2.by \(\chi_{9660}(919, \cdot)\) n/a 2304 2
9660.2.bz \(\chi_{9660}(599, \cdot)\) n/a 4224 2
9660.2.cc \(\chi_{9660}(2209, \cdot)\) n/a 352 2
9660.2.cd \(\chi_{9660}(2069, \cdot)\) n/a 768 2
9660.2.cg \(\chi_{9660}(1241, \cdot)\) n/a 512 2
9660.2.cj \(\chi_{9660}(2851, \cdot)\) n/a 1536 2
9660.2.ck \(\chi_{9660}(2531, \cdot)\) n/a 2816 2
9660.2.cn \(\chi_{9660}(2161, \cdot)\) n/a 256 2
9660.2.co \(\chi_{9660}(5981, \cdot)\) n/a 472 2
9660.2.cr \(\chi_{9660}(691, \cdot)\) n/a 1408 2
9660.2.cs \(\chi_{9660}(551, \cdot)\) n/a 3072 2
9660.2.cv \(\chi_{9660}(5659, \cdot)\) n/a 2112 2
9660.2.cw \(\chi_{9660}(5519, \cdot)\) n/a 4576 2
9660.2.cz \(\chi_{9660}(229, \cdot)\) n/a 384 2
9660.2.da \(\chi_{9660}(4049, \cdot)\) n/a 704 2
9660.2.dc \(\chi_{9660}(841, \cdot)\) n/a 960 10
9660.2.dd \(\chi_{9660}(367, \cdot)\) n/a 4608 4
9660.2.de \(\chi_{9660}(1657, \cdot)\) n/a 704 4
9660.2.dj \(\chi_{9660}(47, \cdot)\) n/a 8448 4
9660.2.dk \(\chi_{9660}(1517, \cdot)\) n/a 1536 4
9660.2.dl \(\chi_{9660}(2713, \cdot)\) n/a 768 4
9660.2.dm \(\chi_{9660}(1243, \cdot)\) n/a 4224 4
9660.2.dr \(\chi_{9660}(737, \cdot)\) n/a 1408 4
9660.2.ds \(\chi_{9660}(1103, \cdot)\) n/a 9152 4
9660.2.dv \(\chi_{9660}(281, \cdot)\) n/a 1920 10
9660.2.dw \(\chi_{9660}(631, \cdot)\) n/a 5760 10
9660.2.dz \(\chi_{9660}(71, \cdot)\) n/a 11520 10
9660.2.ea \(\chi_{9660}(379, \cdot)\) n/a 8640 10
9660.2.ed \(\chi_{9660}(239, \cdot)\) n/a 17280 10
9660.2.ee \(\chi_{9660}(169, \cdot)\) n/a 1440 10
9660.2.eh \(\chi_{9660}(1709, \cdot)\) n/a 2880 10
9660.2.ei \(\chi_{9660}(979, \cdot)\) n/a 11520 10
9660.2.el \(\chi_{9660}(419, \cdot)\) n/a 22880 10
9660.2.em \(\chi_{9660}(769, \cdot)\) n/a 1920 10
9660.2.ep \(\chi_{9660}(209, \cdot)\) n/a 3840 10
9660.2.eq \(\chi_{9660}(181, \cdot)\) n/a 1280 10
9660.2.et \(\chi_{9660}(41, \cdot)\) n/a 2560 10
9660.2.eu \(\chi_{9660}(811, \cdot)\) n/a 7680 10
9660.2.ex \(\chi_{9660}(251, \cdot)\) n/a 15360 10
9660.2.ey \(\chi_{9660}(121, \cdot)\) n/a 2560 20
9660.2.fb \(\chi_{9660}(727, \cdot)\) n/a 23040 20
9660.2.fc \(\chi_{9660}(13, \cdot)\) n/a 3840 20
9660.2.fd \(\chi_{9660}(167, \cdot)\) n/a 45760 20
9660.2.fe \(\chi_{9660}(293, \cdot)\) n/a 7680 20
9660.2.fj \(\chi_{9660}(337, \cdot)\) n/a 2880 20
9660.2.fk \(\chi_{9660}(127, \cdot)\) n/a 17280 20
9660.2.fl \(\chi_{9660}(197, \cdot)\) n/a 5760 20
9660.2.fm \(\chi_{9660}(743, \cdot)\) n/a 34560 20
9660.2.fq \(\chi_{9660}(269, \cdot)\) n/a 7680 20
9660.2.fr \(\chi_{9660}(649, \cdot)\) n/a 3840 20
9660.2.fu \(\chi_{9660}(479, \cdot)\) n/a 45760 20
9660.2.fv \(\chi_{9660}(439, \cdot)\) n/a 23040 20
9660.2.fy \(\chi_{9660}(971, \cdot)\) n/a 30720 20
9660.2.fz \(\chi_{9660}(31, \cdot)\) n/a 15360 20
9660.2.gc \(\chi_{9660}(101, \cdot)\) n/a 5120 20
9660.2.gd \(\chi_{9660}(61, \cdot)\) n/a 2560 20
9660.2.gg \(\chi_{9660}(611, \cdot)\) n/a 30720 20
9660.2.gh \(\chi_{9660}(571, \cdot)\) n/a 15360 20
9660.2.gk \(\chi_{9660}(221, \cdot)\) n/a 5120 20
9660.2.gn \(\chi_{9660}(149, \cdot)\) n/a 7680 20
9660.2.go \(\chi_{9660}(289, \cdot)\) n/a 3840 20
9660.2.gr \(\chi_{9660}(179, \cdot)\) n/a 45760 20
9660.2.gs \(\chi_{9660}(79, \cdot)\) n/a 23040 20
9660.2.gu \(\chi_{9660}(107, \cdot)\) n/a 91520 40
9660.2.gv \(\chi_{9660}(233, \cdot)\) n/a 15360 40
9660.2.ha \(\chi_{9660}(163, \cdot)\) n/a 46080 40
9660.2.hb \(\chi_{9660}(37, \cdot)\) n/a 7680 40
9660.2.hc \(\chi_{9660}(17, \cdot)\) n/a 15360 40
9660.2.hd \(\chi_{9660}(647, \cdot)\) n/a 91520 40
9660.2.hi \(\chi_{9660}(73, \cdot)\) n/a 7680 40
9660.2.hj \(\chi_{9660}(103, \cdot)\) n/a 46080 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9660))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9660)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(644))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(805))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(966))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1610))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1932))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2415))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4830))\)\(^{\oplus 2}\)