# Properties

 Label 9702.2 Level 9702 Weight 2 Dimension 632525 Nonzero newspaces 80 Sturm bound 10160640

## Defining parameters

 Level: $$N$$ = $$9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$10160640$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9702))$$.

Total New Old
Modular forms 2559360 632525 1926835
Cusp forms 2520961 632525 1888436
Eisenstein series 38399 0 38399

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9702))$$

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
9702.2.a $$\chi_{9702}(1, \cdot)$$ 9702.2.a.a 1 1
9702.2.a.b 1
9702.2.a.c 1
9702.2.a.d 1
9702.2.a.e 1
9702.2.a.f 1
9702.2.a.g 1
9702.2.a.h 1
9702.2.a.i 1
9702.2.a.j 1
9702.2.a.k 1
9702.2.a.l 1
9702.2.a.m 1
9702.2.a.n 1
9702.2.a.o 1
9702.2.a.p 1
9702.2.a.q 1
9702.2.a.r 1
9702.2.a.s 1
9702.2.a.t 1
9702.2.a.u 1
9702.2.a.v 1
9702.2.a.w 1
9702.2.a.x 1
9702.2.a.y 1
9702.2.a.z 1
9702.2.a.ba 1
9702.2.a.bb 1
9702.2.a.bc 1
9702.2.a.bd 1
9702.2.a.be 1
9702.2.a.bf 1
9702.2.a.bg 1
9702.2.a.bh 1
9702.2.a.bi 1
9702.2.a.bj 1
9702.2.a.bk 1
9702.2.a.bl 1
9702.2.a.bm 1
9702.2.a.bn 1
9702.2.a.bo 1
9702.2.a.bp 1
9702.2.a.bq 1
9702.2.a.br 1
9702.2.a.bs 1
9702.2.a.bt 1
9702.2.a.bu 1
9702.2.a.bv 1
9702.2.a.bw 1
9702.2.a.bx 1
9702.2.a.by 1
9702.2.a.bz 1
9702.2.a.ca 1
9702.2.a.cb 1
9702.2.a.cc 1
9702.2.a.cd 1
9702.2.a.ce 1
9702.2.a.cf 1
9702.2.a.cg 1
9702.2.a.ch 2
9702.2.a.ci 2
9702.2.a.cj 2
9702.2.a.ck 2
9702.2.a.cl 2
9702.2.a.cm 2
9702.2.a.cn 2
9702.2.a.co 2
9702.2.a.cp 2
9702.2.a.cq 2
9702.2.a.cr 2
9702.2.a.cs 2
9702.2.a.ct 2
9702.2.a.cu 2
9702.2.a.cv 2
9702.2.a.cw 2
9702.2.a.cx 2
9702.2.a.cy 2
9702.2.a.cz 2
9702.2.a.da 2
9702.2.a.db 2
9702.2.a.dc 2
9702.2.a.dd 2
9702.2.a.de 2
9702.2.a.df 2
9702.2.a.dg 2
9702.2.a.dh 2
9702.2.a.di 2
9702.2.a.dj 2
9702.2.a.dk 2
9702.2.a.dl 2
9702.2.a.dm 2
9702.2.a.dn 2
9702.2.a.do 2
9702.2.a.dp 2
9702.2.a.dq 2
9702.2.a.dr 2
9702.2.a.ds 2
9702.2.a.dt 3
9702.2.a.du 3
9702.2.a.dv 3
9702.2.a.dw 3
9702.2.a.dx 3
9702.2.a.dy 3
9702.2.a.dz 4
9702.2.a.ea 4
9702.2.a.eb 4
9702.2.a.ec 4
9702.2.c $$\chi_{9702}(197, \cdot)$$ n/a 164 1
9702.2.e $$\chi_{9702}(8623, \cdot)$$ n/a 200 1
9702.2.g $$\chi_{9702}(881, \cdot)$$ n/a 128 1
9702.2.i $$\chi_{9702}(1255, \cdot)$$ n/a 800 2
9702.2.j $$\chi_{9702}(3235, \cdot)$$ n/a 820 2
9702.2.k $$\chi_{9702}(6535, \cdot)$$ n/a 336 2
9702.2.l $$\chi_{9702}(67, \cdot)$$ n/a 800 2
9702.2.m $$\chi_{9702}(883, \cdot)$$ n/a 820 4
9702.2.n $$\chi_{9702}(5323, \cdot)$$ n/a 960 2
9702.2.p $$\chi_{9702}(1451, \cdot)$$ n/a 960 2
9702.2.r $$\chi_{9702}(2861, \cdot)$$ n/a 272 2
9702.2.w $$\chi_{9702}(7283, \cdot)$$ n/a 800 2
9702.2.y $$\chi_{9702}(4115, \cdot)$$ n/a 800 2
9702.2.ba $$\chi_{9702}(6731, \cdot)$$ n/a 320 2
9702.2.bd $$\chi_{9702}(4135, \cdot)$$ n/a 960 2
9702.2.bf $$\chi_{9702}(2155, \cdot)$$ n/a 960 2
9702.2.bh $$\chi_{9702}(263, \cdot)$$ n/a 960 2
9702.2.bj $$\chi_{9702}(3431, \cdot)$$ n/a 984 2
9702.2.bk $$\chi_{9702}(901, \cdot)$$ n/a 400 2
9702.2.bn $$\chi_{9702}(815, \cdot)$$ n/a 800 2
9702.2.bp $$\chi_{9702}(1387, \cdot)$$ n/a 1416 6
9702.2.br $$\chi_{9702}(1763, \cdot)$$ n/a 640 4
9702.2.bt $$\chi_{9702}(2449, \cdot)$$ n/a 800 4
9702.2.bv $$\chi_{9702}(3725, \cdot)$$ n/a 656 4
9702.2.by $$\chi_{9702}(2267, \cdot)$$ n/a 1152 6
9702.2.ca $$\chi_{9702}(307, \cdot)$$ n/a 1680 6
9702.2.cc $$\chi_{9702}(1583, \cdot)$$ n/a 1344 6
9702.2.ce $$\chi_{9702}(949, \cdot)$$ n/a 3840 8
9702.2.cf $$\chi_{9702}(361, \cdot)$$ n/a 1600 8
9702.2.cg $$\chi_{9702}(295, \cdot)$$ n/a 3936 8
9702.2.ch $$\chi_{9702}(2137, \cdot)$$ n/a 3840 8
9702.2.ci $$\chi_{9702}(331, \cdot)$$ n/a 6720 12
9702.2.cj $$\chi_{9702}(793, \cdot)$$ n/a 2784 12
9702.2.ck $$\chi_{9702}(463, \cdot)$$ n/a 6720 12
9702.2.cl $$\chi_{9702}(529, \cdot)$$ n/a 6720 12
9702.2.cn $$\chi_{9702}(1697, \cdot)$$ n/a 3840 8
9702.2.cq $$\chi_{9702}(19, \cdot)$$ n/a 1600 8
9702.2.cr $$\chi_{9702}(491, \cdot)$$ n/a 3936 8
9702.2.ct $$\chi_{9702}(1157, \cdot)$$ n/a 3840 8
9702.2.cv $$\chi_{9702}(391, \cdot)$$ n/a 3840 8
9702.2.cx $$\chi_{9702}(607, \cdot)$$ n/a 3840 8
9702.2.da $$\chi_{9702}(557, \cdot)$$ n/a 1280 8
9702.2.dc $$\chi_{9702}(587, \cdot)$$ n/a 3840 8
9702.2.de $$\chi_{9702}(509, \cdot)$$ n/a 3840 8
9702.2.dj $$\chi_{9702}(521, \cdot)$$ n/a 1280 8
9702.2.dl $$\chi_{9702}(569, \cdot)$$ n/a 3840 8
9702.2.dn $$\chi_{9702}(1195, \cdot)$$ n/a 3840 8
9702.2.do $$\chi_{9702}(379, \cdot)$$ n/a 6720 24
9702.2.dq $$\chi_{9702}(551, \cdot)$$ n/a 6720 12
9702.2.dt $$\chi_{9702}(703, \cdot)$$ n/a 3360 12
9702.2.du $$\chi_{9702}(659, \cdot)$$ n/a 8064 12
9702.2.dw $$\chi_{9702}(527, \cdot)$$ n/a 8064 12
9702.2.dy $$\chi_{9702}(769, \cdot)$$ n/a 8064 12
9702.2.ea $$\chi_{9702}(241, \cdot)$$ n/a 8064 12
9702.2.ed $$\chi_{9702}(989, \cdot)$$ n/a 2688 12
9702.2.ef $$\chi_{9702}(419, \cdot)$$ n/a 6720 12
9702.2.eh $$\chi_{9702}(353, \cdot)$$ n/a 6720 12
9702.2.em $$\chi_{9702}(89, \cdot)$$ n/a 2208 12
9702.2.eo $$\chi_{9702}(65, \cdot)$$ n/a 8064 12
9702.2.eq $$\chi_{9702}(439, \cdot)$$ n/a 8064 12
9702.2.es $$\chi_{9702}(701, \cdot)$$ n/a 5376 24
9702.2.eu $$\chi_{9702}(811, \cdot)$$ n/a 6720 24
9702.2.ew $$\chi_{9702}(125, \cdot)$$ n/a 5376 24
9702.2.ey $$\chi_{9702}(25, \cdot)$$ n/a 32256 48
9702.2.ez $$\chi_{9702}(169, \cdot)$$ n/a 32256 48
9702.2.fa $$\chi_{9702}(37, \cdot)$$ n/a 13440 48
9702.2.fb $$\chi_{9702}(445, \cdot)$$ n/a 32256 48
9702.2.fc $$\chi_{9702}(61, \cdot)$$ n/a 32256 48
9702.2.fe $$\chi_{9702}(95, \cdot)$$ n/a 32256 48
9702.2.fg $$\chi_{9702}(269, \cdot)$$ n/a 10752 48
9702.2.fl $$\chi_{9702}(5, \cdot)$$ n/a 32256 48
9702.2.fn $$\chi_{9702}(335, \cdot)$$ n/a 32256 48
9702.2.fp $$\chi_{9702}(107, \cdot)$$ n/a 10752 48
9702.2.fs $$\chi_{9702}(481, \cdot)$$ n/a 32256 48
9702.2.fu $$\chi_{9702}(13, \cdot)$$ n/a 32256 48
9702.2.fw $$\chi_{9702}(149, \cdot)$$ n/a 32256 48
9702.2.fy $$\chi_{9702}(29, \cdot)$$ n/a 32256 48
9702.2.fz $$\chi_{9702}(73, \cdot)$$ n/a 13440 48
9702.2.gc $$\chi_{9702}(47, \cdot)$$ n/a 32256 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9702))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9702)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(198))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(462))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(693))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(882))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1078))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1386))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1617))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3234))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4851))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9702))$$$$^{\oplus 1}$$