Properties

Label 9405.2
Level 9405
Weight 2
Dimension 2198988
Nonzero newspaces 192
Sturm bound 12441600

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Defining parameters

Level: \( N \) = \( 9405 = 3^{2} \cdot 5 \cdot 11 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 192 \)
Sturm bound: \(12441600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9405))\).

Total New Old
Modular forms 3133440 2215508 917932
Cusp forms 3087361 2198988 888373
Eisenstein series 46079 16520 29559

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9405))\)

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
9405.2.a \(\chi_{9405}(1, \cdot)\) 9405.2.a.a 1 1
9405.2.a.b 1
9405.2.a.c 1
9405.2.a.d 1
9405.2.a.e 1
9405.2.a.f 1
9405.2.a.g 1
9405.2.a.h 1
9405.2.a.i 1
9405.2.a.j 1
9405.2.a.k 1
9405.2.a.l 1
9405.2.a.m 1
9405.2.a.n 1
9405.2.a.o 2
9405.2.a.p 3
9405.2.a.q 3
9405.2.a.r 3
9405.2.a.s 3
9405.2.a.t 4
9405.2.a.u 5
9405.2.a.v 5
9405.2.a.w 6
9405.2.a.x 6
9405.2.a.y 6
9405.2.a.z 6
9405.2.a.ba 6
9405.2.a.bb 7
9405.2.a.bc 7
9405.2.a.bd 7
9405.2.a.be 7
9405.2.a.bf 8
9405.2.a.bg 9
9405.2.a.bh 9
9405.2.a.bi 9
9405.2.a.bj 9
9405.2.a.bk 9
9405.2.a.bl 9
9405.2.a.bm 10
9405.2.a.bn 10
9405.2.a.bo 10
9405.2.a.bp 12
9405.2.a.bq 14
9405.2.a.br 14
9405.2.a.bs 15
9405.2.a.bt 15
9405.2.a.bu 19
9405.2.a.bv 19
9405.2.b \(\chi_{9405}(5644, \cdot)\) n/a 452 1
9405.2.e \(\chi_{9405}(2564, \cdot)\) n/a 400 1
9405.2.f \(\chi_{9405}(2089, \cdot)\) n/a 596 1
9405.2.i \(\chi_{9405}(989, \cdot)\) n/a 432 1
9405.2.j \(\chi_{9405}(4751, \cdot)\) n/a 288 1
9405.2.m \(\chi_{9405}(5851, \cdot)\) n/a 400 1
9405.2.n \(\chi_{9405}(6326, \cdot)\) n/a 272 1
9405.2.q \(\chi_{9405}(3136, \cdot)\) n/a 1440 2
9405.2.r \(\chi_{9405}(1816, \cdot)\) n/a 1600 2
9405.2.s \(\chi_{9405}(2971, \cdot)\) n/a 672 2
9405.2.t \(\chi_{9405}(8086, \cdot)\) n/a 1600 2
9405.2.v \(\chi_{9405}(5642, \cdot)\) n/a 960 2
9405.2.x \(\chi_{9405}(1198, \cdot)\) n/a 1080 2
9405.2.z \(\chi_{9405}(1673, \cdot)\) n/a 720 2
9405.2.bb \(\chi_{9405}(892, \cdot)\) n/a 1000 2
9405.2.bc \(\chi_{9405}(856, \cdot)\) n/a 1440 4
9405.2.bd \(\chi_{9405}(274, \cdot)\) n/a 2864 2
9405.2.bg \(\chi_{9405}(2804, \cdot)\) n/a 2864 2
9405.2.bh \(\chi_{9405}(4324, \cdot)\) n/a 2400 2
9405.2.bk \(\chi_{9405}(2729, \cdot)\) n/a 2400 2
9405.2.bl \(\chi_{9405}(901, \cdot)\) n/a 800 2
9405.2.bo \(\chi_{9405}(296, \cdot)\) n/a 640 2
9405.2.bs \(\chi_{9405}(56, \cdot)\) n/a 1600 2
9405.2.bu \(\chi_{9405}(221, \cdot)\) n/a 1600 2
9405.2.bv \(\chi_{9405}(6016, \cdot)\) n/a 1920 2
9405.2.bx \(\chi_{9405}(2716, \cdot)\) n/a 1920 2
9405.2.ca \(\chi_{9405}(3431, \cdot)\) n/a 1920 2
9405.2.cc \(\chi_{9405}(1616, \cdot)\) n/a 1728 2
9405.2.cf \(\chi_{9405}(1376, \cdot)\) n/a 544 2
9405.2.cg \(\chi_{9405}(7019, \cdot)\) n/a 800 2
9405.2.cj \(\chi_{9405}(1189, \cdot)\) n/a 1000 2
9405.2.ck \(\chi_{9405}(824, \cdot)\) n/a 2864 2
9405.2.cm \(\chi_{9405}(4124, \cdot)\) n/a 2592 2
9405.2.cp \(\chi_{9405}(2254, \cdot)\) n/a 2864 2
9405.2.cr \(\chi_{9405}(5224, \cdot)\) n/a 2864 2
9405.2.cs \(\chi_{9405}(5699, \cdot)\) n/a 2400 2
9405.2.cu \(\chi_{9405}(749, \cdot)\) n/a 2400 2
9405.2.cx \(\chi_{9405}(2509, \cdot)\) n/a 2160 2
9405.2.cz \(\chi_{9405}(2344, \cdot)\) n/a 2400 2
9405.2.da \(\chi_{9405}(3959, \cdot)\) n/a 960 2
9405.2.dd \(\chi_{9405}(6544, \cdot)\) n/a 1192 2
9405.2.de \(\chi_{9405}(6491, \cdot)\) n/a 1600 2
9405.2.dh \(\chi_{9405}(1451, \cdot)\) n/a 1920 2
9405.2.dk \(\chi_{9405}(4036, \cdot)\) n/a 1920 2
9405.2.dl \(\chi_{9405}(1486, \cdot)\) n/a 1992 6
9405.2.dm \(\chi_{9405}(826, \cdot)\) n/a 4800 6
9405.2.dn \(\chi_{9405}(4291, \cdot)\) n/a 4800 6
9405.2.dp \(\chi_{9405}(2051, \cdot)\) n/a 1280 4
9405.2.ds \(\chi_{9405}(721, \cdot)\) n/a 1600 4
9405.2.dt \(\chi_{9405}(2186, \cdot)\) n/a 1152 4
9405.2.dw \(\chi_{9405}(134, \cdot)\) n/a 1728 4
9405.2.dx \(\chi_{9405}(1234, \cdot)\) n/a 2384 4
9405.2.ea \(\chi_{9405}(1709, \cdot)\) n/a 1920 4
9405.2.eb \(\chi_{9405}(1369, \cdot)\) n/a 2160 4
9405.2.ed \(\chi_{9405}(1607, \cdot)\) n/a 4800 4
9405.2.ef \(\chi_{9405}(958, \cdot)\) n/a 4800 4
9405.2.eh \(\chi_{9405}(5807, \cdot)\) n/a 5728 4
9405.2.ej \(\chi_{9405}(1033, \cdot)\) n/a 5728 4
9405.2.em \(\chi_{9405}(1418, \cdot)\) n/a 5728 4
9405.2.eo \(\chi_{9405}(1132, \cdot)\) n/a 5728 4
9405.2.ep \(\chi_{9405}(2927, \cdot)\) n/a 4320 4
9405.2.eq \(\chi_{9405}(2762, \cdot)\) n/a 1600 4
9405.2.et \(\chi_{9405}(5347, \cdot)\) n/a 2000 4
9405.2.eu \(\chi_{9405}(4027, \cdot)\) n/a 4800 4
9405.2.ex \(\chi_{9405}(692, \cdot)\) n/a 1920 4
9405.2.ey \(\chi_{9405}(1253, \cdot)\) n/a 5728 4
9405.2.fb \(\chi_{9405}(2452, \cdot)\) n/a 5184 4
9405.2.fc \(\chi_{9405}(2287, \cdot)\) n/a 2384 4
9405.2.fg \(\chi_{9405}(353, \cdot)\) n/a 4800 4
9405.2.fi \(\chi_{9405}(1057, \cdot)\) n/a 4800 4
9405.2.fj \(\chi_{9405}(691, \cdot)\) n/a 7680 8
9405.2.fk \(\chi_{9405}(676, \cdot)\) n/a 3200 8
9405.2.fl \(\chi_{9405}(961, \cdot)\) n/a 7680 8
9405.2.fm \(\chi_{9405}(1996, \cdot)\) n/a 6912 8
9405.2.fn \(\chi_{9405}(736, \cdot)\) n/a 5760 6
9405.2.fq \(\chi_{9405}(461, \cdot)\) n/a 5760 6
9405.2.fr \(\chi_{9405}(529, \cdot)\) n/a 7200 6
9405.2.fu \(\chi_{9405}(3719, \cdot)\) n/a 7200 6
9405.2.fx \(\chi_{9405}(1211, \cdot)\) n/a 4800 6
9405.2.fz \(\chi_{9405}(2366, \cdot)\) n/a 1584 6
9405.2.gc \(\chi_{9405}(3244, \cdot)\) n/a 8592 6
9405.2.ge \(\chi_{9405}(109, \cdot)\) n/a 3576 6
9405.2.gf \(\chi_{9405}(2474, \cdot)\) n/a 2880 6
9405.2.gh \(\chi_{9405}(5279, \cdot)\) n/a 8592 6
9405.2.gj \(\chi_{9405}(241, \cdot)\) n/a 5760 6
9405.2.gl \(\chi_{9405}(1891, \cdot)\) n/a 2400 6
9405.2.go \(\chi_{9405}(2771, \cdot)\) n/a 1920 6
9405.2.gq \(\chi_{9405}(131, \cdot)\) n/a 5760 6
9405.2.gr \(\chi_{9405}(199, \cdot)\) n/a 3000 6
9405.2.gt \(\chi_{9405}(1354, \cdot)\) n/a 7200 6
9405.2.gw \(\chi_{9405}(914, \cdot)\) n/a 7200 6
9405.2.gy \(\chi_{9405}(89, \cdot)\) n/a 2400 6
9405.2.ha \(\chi_{9405}(716, \cdot)\) n/a 4800 6
9405.2.hd \(\chi_{9405}(439, \cdot)\) n/a 8592 6
9405.2.he \(\chi_{9405}(329, \cdot)\) n/a 8592 6
9405.2.hg \(\chi_{9405}(37, \cdot)\) n/a 4768 8
9405.2.hi \(\chi_{9405}(647, \cdot)\) n/a 3456 8
9405.2.hk \(\chi_{9405}(172, \cdot)\) n/a 4320 8
9405.2.hm \(\chi_{9405}(512, \cdot)\) n/a 3840 8
9405.2.hp \(\chi_{9405}(601, \cdot)\) n/a 7680 8
9405.2.hq \(\chi_{9405}(596, \cdot)\) n/a 7680 8
9405.2.ht \(\chi_{9405}(806, \cdot)\) n/a 7680 8
9405.2.hw \(\chi_{9405}(1414, \cdot)\) n/a 4768 8
9405.2.hx \(\chi_{9405}(809, \cdot)\) n/a 3840 8
9405.2.ia \(\chi_{9405}(619, \cdot)\) n/a 11456 8
9405.2.ic \(\chi_{9405}(229, \cdot)\) n/a 10368 8
9405.2.id \(\chi_{9405}(1589, \cdot)\) n/a 11456 8
9405.2.if \(\chi_{9405}(284, \cdot)\) n/a 11456 8
9405.2.ii \(\chi_{9405}(94, \cdot)\) n/a 11456 8
9405.2.ik \(\chi_{9405}(844, \cdot)\) n/a 11456 8
9405.2.il \(\chi_{9405}(1559, \cdot)\) n/a 10368 8
9405.2.in \(\chi_{9405}(524, \cdot)\) n/a 11456 8
9405.2.iq \(\chi_{9405}(64, \cdot)\) n/a 4768 8
9405.2.ir \(\chi_{9405}(179, \cdot)\) n/a 3840 8
9405.2.iu \(\chi_{9405}(521, \cdot)\) n/a 2560 8
9405.2.ix \(\chi_{9405}(761, \cdot)\) n/a 6912 8
9405.2.iz \(\chi_{9405}(866, \cdot)\) n/a 7680 8
9405.2.ja \(\chi_{9405}(151, \cdot)\) n/a 7680 8
9405.2.jc \(\chi_{9405}(886, \cdot)\) n/a 7680 8
9405.2.jf \(\chi_{9405}(236, \cdot)\) n/a 7680 8
9405.2.jh \(\chi_{9405}(911, \cdot)\) n/a 7680 8
9405.2.jl \(\chi_{9405}(1151, \cdot)\) n/a 2560 8
9405.2.jm \(\chi_{9405}(46, \cdot)\) n/a 3200 8
9405.2.jp \(\chi_{9405}(1874, \cdot)\) n/a 11456 8
9405.2.jq \(\chi_{9405}(49, \cdot)\) n/a 11456 8
9405.2.jt \(\chi_{9405}(239, \cdot)\) n/a 11456 8
9405.2.ju \(\chi_{9405}(259, \cdot)\) n/a 11456 8
9405.2.jx \(\chi_{9405}(2047, \cdot)\) n/a 14400 12
9405.2.ka \(\chi_{9405}(43, \cdot)\) n/a 17184 12
9405.2.kb \(\chi_{9405}(802, \cdot)\) n/a 7152 12
9405.2.ke \(\chi_{9405}(67, \cdot)\) n/a 14400 12
9405.2.kf \(\chi_{9405}(298, \cdot)\) n/a 6000 12
9405.2.kh \(\chi_{9405}(142, \cdot)\) n/a 17184 12
9405.2.ki \(\chi_{9405}(527, \cdot)\) n/a 17184 12
9405.2.kk \(\chi_{9405}(23, \cdot)\) n/a 14400 12
9405.2.kl \(\chi_{9405}(188, \cdot)\) n/a 4800 12
9405.2.ko \(\chi_{9405}(32, \cdot)\) n/a 17184 12
9405.2.kp \(\chi_{9405}(98, \cdot)\) n/a 5760 12
9405.2.ks \(\chi_{9405}(518, \cdot)\) n/a 14400 12
9405.2.ku \(\chi_{9405}(16, \cdot)\) n/a 23040 24
9405.2.kv \(\chi_{9405}(196, \cdot)\) n/a 23040 24
9405.2.kw \(\chi_{9405}(586, \cdot)\) n/a 9600 24
9405.2.kx \(\chi_{9405}(202, \cdot)\) n/a 22912 16
9405.2.kz \(\chi_{9405}(482, \cdot)\) n/a 22912 16
9405.2.ld \(\chi_{9405}(1018, \cdot)\) n/a 9536 16
9405.2.le \(\chi_{9405}(457, \cdot)\) n/a 20736 16
9405.2.lh \(\chi_{9405}(227, \cdot)\) n/a 22912 16
9405.2.li \(\chi_{9405}(8, \cdot)\) n/a 7680 16
9405.2.ll \(\chi_{9405}(322, \cdot)\) n/a 22912 16
9405.2.lm \(\chi_{9405}(388, \cdot)\) n/a 9536 16
9405.2.lp \(\chi_{9405}(368, \cdot)\) n/a 7680 16
9405.2.lq \(\chi_{9405}(533, \cdot)\) n/a 20736 16
9405.2.lr \(\chi_{9405}(277, \cdot)\) n/a 22912 16
9405.2.lt \(\chi_{9405}(392, \cdot)\) n/a 22912 16
9405.2.lw \(\chi_{9405}(7, \cdot)\) n/a 22912 16
9405.2.ly \(\chi_{9405}(293, \cdot)\) n/a 22912 16
9405.2.ma \(\chi_{9405}(103, \cdot)\) n/a 22912 16
9405.2.mc \(\chi_{9405}(752, \cdot)\) n/a 22912 16
9405.2.me \(\chi_{9405}(74, \cdot)\) n/a 34368 24
9405.2.mf \(\chi_{9405}(79, \cdot)\) n/a 34368 24
9405.2.mi \(\chi_{9405}(86, \cdot)\) n/a 23040 24
9405.2.mk \(\chi_{9405}(224, \cdot)\) n/a 11520 24
9405.2.mm \(\chi_{9405}(14, \cdot)\) n/a 34368 24
9405.2.mp \(\chi_{9405}(454, \cdot)\) n/a 34368 24
9405.2.mr \(\chi_{9405}(289, \cdot)\) n/a 14304 24
9405.2.ms \(\chi_{9405}(101, \cdot)\) n/a 23040 24
9405.2.mu \(\chi_{9405}(161, \cdot)\) n/a 7680 24
9405.2.mx \(\chi_{9405}(811, \cdot)\) n/a 9600 24
9405.2.mz \(\chi_{9405}(211, \cdot)\) n/a 23040 24
9405.2.nb \(\chi_{9405}(149, \cdot)\) n/a 34368 24
9405.2.nd \(\chi_{9405}(359, \cdot)\) n/a 11520 24
9405.2.ne \(\chi_{9405}(469, \cdot)\) n/a 14304 24
9405.2.ng \(\chi_{9405}(679, \cdot)\) n/a 34368 24
9405.2.nj \(\chi_{9405}(71, \cdot)\) n/a 7680 24
9405.2.nl \(\chi_{9405}(146, \cdot)\) n/a 23040 24
9405.2.no \(\chi_{9405}(344, \cdot)\) n/a 34368 24
9405.2.nr \(\chi_{9405}(4, \cdot)\) n/a 34368 24
9405.2.ns \(\chi_{9405}(446, \cdot)\) n/a 23040 24
9405.2.nv \(\chi_{9405}(1381, \cdot)\) n/a 23040 24
9405.2.nx \(\chi_{9405}(47, \cdot)\) n/a 68736 48
9405.2.oa \(\chi_{9405}(413, \cdot)\) n/a 23040 48
9405.2.ob \(\chi_{9405}(2, \cdot)\) n/a 68736 48
9405.2.oe \(\chi_{9405}(377, \cdot)\) n/a 23040 48
9405.2.of \(\chi_{9405}(92, \cdot)\) n/a 68736 48
9405.2.oh \(\chi_{9405}(623, \cdot)\) n/a 68736 48
9405.2.oi \(\chi_{9405}(112, \cdot)\) n/a 68736 48
9405.2.ok \(\chi_{9405}(262, \cdot)\) n/a 28608 48
9405.2.ol \(\chi_{9405}(97, \cdot)\) n/a 68736 48
9405.2.oo \(\chi_{9405}(28, \cdot)\) n/a 28608 48
9405.2.op \(\chi_{9405}(358, \cdot)\) n/a 68736 48
9405.2.os \(\chi_{9405}(412, \cdot)\) n/a 68736 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9405))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9405)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1045))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1881))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9405))\)\(^{\oplus 1}\)