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Properties

Label 9996.2
Level 9996
Weight 2
Dimension 1126720
Nonzero newspaces 80
Sturm bound 10838016

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Defining parameters

Level: \( N \) = \( 9996 = 2^{2} \cdot 3 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(10838016\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9996))\).

Total New Old
Modular forms 2728704 1132536 1596168
Cusp forms 2690305 1126720 1563585
Eisenstein series 38399 5816 32583

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9996))\)

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
9996.2.a \(\chi_{9996}(1, \cdot)\) 9996.2.a.a 1 1
9996.2.a.b 1
9996.2.a.c 1
9996.2.a.d 1
9996.2.a.e 1
9996.2.a.f 1
9996.2.a.g 1
9996.2.a.h 1
9996.2.a.i 1
9996.2.a.j 1
9996.2.a.k 1
9996.2.a.l 1
9996.2.a.m 1
9996.2.a.n 1
9996.2.a.o 1
9996.2.a.p 1
9996.2.a.q 1
9996.2.a.r 2
9996.2.a.s 2
9996.2.a.t 2
9996.2.a.u 2
9996.2.a.v 2
9996.2.a.w 2
9996.2.a.x 3
9996.2.a.y 4
9996.2.a.z 4
9996.2.a.ba 4
9996.2.a.bb 4
9996.2.a.bc 4
9996.2.a.bd 4
9996.2.a.be 5
9996.2.a.bf 5
9996.2.a.bg 6
9996.2.a.bh 6
9996.2.a.bi 6
9996.2.a.bj 6
9996.2.a.bk 10
9996.2.a.bl 10
9996.2.c \(\chi_{9996}(7447, \cdot)\) n/a 640 1
9996.2.d \(\chi_{9996}(5881, \cdot)\) n/a 122 1
9996.2.g \(\chi_{9996}(4997, \cdot)\) n/a 240 1
9996.2.h \(\chi_{9996}(1667, \cdot)\) n/a 1312 1
9996.2.j \(\chi_{9996}(9113, \cdot)\) n/a 212 1
9996.2.m \(\chi_{9996}(7547, \cdot)\) n/a 1456 1
9996.2.n \(\chi_{9996}(3331, \cdot)\) n/a 720 1
9996.2.q \(\chi_{9996}(4489, \cdot)\) n/a 212 2
9996.2.s \(\chi_{9996}(2155, \cdot)\) n/a 1440 2
9996.2.u \(\chi_{9996}(293, \cdot)\) n/a 480 2
9996.2.w \(\chi_{9996}(1177, \cdot)\) n/a 244 2
9996.2.y \(\chi_{9996}(2843, \cdot)\) n/a 2912 2
9996.2.ba \(\chi_{9996}(4147, \cdot)\) n/a 1440 2
9996.2.bd \(\chi_{9996}(4625, \cdot)\) n/a 428 2
9996.2.be \(\chi_{9996}(2039, \cdot)\) n/a 2848 2
9996.2.bg \(\chi_{9996}(509, \cdot)\) n/a 480 2
9996.2.bj \(\chi_{9996}(851, \cdot)\) n/a 2560 2
9996.2.bk \(\chi_{9996}(2959, \cdot)\) n/a 1280 2
9996.2.bn \(\chi_{9996}(373, \cdot)\) n/a 240 2
9996.2.bo \(\chi_{9996}(1429, \cdot)\) n/a 888 6
9996.2.bp \(\chi_{9996}(6469, \cdot)\) n/a 496 4
9996.2.bq \(\chi_{9996}(491, \cdot)\) n/a 5824 4
9996.2.bt \(\chi_{9996}(3919, \cdot)\) n/a 2880 4
9996.2.bu \(\chi_{9996}(5585, \cdot)\) n/a 960 4
9996.2.bx \(\chi_{9996}(1109, \cdot)\) n/a 960 4
9996.2.bz \(\chi_{9996}(2971, \cdot)\) n/a 2880 4
9996.2.cb \(\chi_{9996}(863, \cdot)\) n/a 5696 4
9996.2.cd \(\chi_{9996}(361, \cdot)\) n/a 480 4
9996.2.cg \(\chi_{9996}(475, \cdot)\) n/a 6048 6
9996.2.cj \(\chi_{9996}(407, \cdot)\) n/a 12048 6
9996.2.ck \(\chi_{9996}(545, \cdot)\) n/a 1800 6
9996.2.cm \(\chi_{9996}(239, \cdot)\) n/a 10752 6
9996.2.cp \(\chi_{9996}(713, \cdot)\) n/a 2016 6
9996.2.cq \(\chi_{9996}(169, \cdot)\) n/a 1008 6
9996.2.ct \(\chi_{9996}(307, \cdot)\) n/a 5376 6
9996.2.cw \(\chi_{9996}(97, \cdot)\) n/a 960 8
9996.2.cx \(\chi_{9996}(197, \cdot)\) n/a 1968 8
9996.2.cy \(\chi_{9996}(295, \cdot)\) n/a 5904 8
9996.2.cz \(\chi_{9996}(1763, \cdot)\) n/a 11392 8
9996.2.dc \(\chi_{9996}(205, \cdot)\) n/a 1800 12
9996.2.df \(\chi_{9996}(961, \cdot)\) n/a 960 8
9996.2.dg \(\chi_{9996}(263, \cdot)\) n/a 11392 8
9996.2.dj \(\chi_{9996}(19, \cdot)\) n/a 5760 8
9996.2.dk \(\chi_{9996}(1097, \cdot)\) n/a 1920 8
9996.2.dl \(\chi_{9996}(421, \cdot)\) n/a 2016 12
9996.2.dn \(\chi_{9996}(659, \cdot)\) n/a 24096 12
9996.2.dp \(\chi_{9996}(55, \cdot)\) n/a 12096 12
9996.2.dr \(\chi_{9996}(965, \cdot)\) n/a 4032 12
9996.2.du \(\chi_{9996}(781, \cdot)\) n/a 2016 12
9996.2.dv \(\chi_{9996}(103, \cdot)\) n/a 10752 12
9996.2.dy \(\chi_{9996}(443, \cdot)\) n/a 21504 12
9996.2.dz \(\chi_{9996}(101, \cdot)\) n/a 4032 12
9996.2.eb \(\chi_{9996}(611, \cdot)\) n/a 24096 12
9996.2.ee \(\chi_{9996}(341, \cdot)\) n/a 3576 12
9996.2.eh \(\chi_{9996}(271, \cdot)\) n/a 12096 12
9996.2.ek \(\chi_{9996}(215, \cdot)\) n/a 22784 16
9996.2.el \(\chi_{9996}(79, \cdot)\) n/a 11520 16
9996.2.em \(\chi_{9996}(1145, \cdot)\) n/a 3840 16
9996.2.en \(\chi_{9996}(313, \cdot)\) n/a 1920 16
9996.2.es \(\chi_{9996}(461, \cdot)\) n/a 8064 24
9996.2.et \(\chi_{9996}(223, \cdot)\) n/a 24192 24
9996.2.ew \(\chi_{9996}(155, \cdot)\) n/a 48192 24
9996.2.ex \(\chi_{9996}(253, \cdot)\) n/a 4032 24
9996.2.ez \(\chi_{9996}(191, \cdot)\) n/a 48192 24
9996.2.fb \(\chi_{9996}(625, \cdot)\) n/a 4032 24
9996.2.fd \(\chi_{9996}(89, \cdot)\) n/a 8064 24
9996.2.ff \(\chi_{9996}(115, \cdot)\) n/a 24192 24
9996.2.fg \(\chi_{9996}(29, \cdot)\) n/a 16128 48
9996.2.fh \(\chi_{9996}(181, \cdot)\) n/a 8064 48
9996.2.fm \(\chi_{9996}(167, \cdot)\) n/a 96384 48
9996.2.fn \(\chi_{9996}(211, \cdot)\) n/a 48384 48
9996.2.fo \(\chi_{9996}(185, \cdot)\) n/a 16128 48
9996.2.fp \(\chi_{9996}(355, \cdot)\) n/a 48384 48
9996.2.fs \(\chi_{9996}(179, \cdot)\) n/a 96384 48
9996.2.ft \(\chi_{9996}(25, \cdot)\) n/a 8064 48
9996.2.fw \(\chi_{9996}(163, \cdot)\) n/a 96768 96
9996.2.fx \(\chi_{9996}(131, \cdot)\) n/a 192768 96
9996.2.gc \(\chi_{9996}(61, \cdot)\) n/a 16128 96
9996.2.gd \(\chi_{9996}(65, \cdot)\) n/a 32256 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9996))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9996)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(714))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(833))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1428))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1666))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2499))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3332))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4998))\)\(^{\oplus 2}\)