# Properties

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

## 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

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