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Properties

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

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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

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