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Properties

Label 12996.2
Level 12996
Weight 2
Dimension 2144416
Nonzero newspaces 64
Sturm bound 18714240

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Defining parameters

Level: \( N \) = \( 12996 = 2^{2} \cdot 3^{2} \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(18714240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(12996))\).

Total New Old
Modular forms 4698720 2152848 2545872
Cusp forms 4658401 2144416 2513985
Eisenstein series 40319 8432 31887

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(12996))\)

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
12996.2.a \(\chi_{12996}(1, \cdot)\) 12996.2.a.a 1 1
12996.2.a.b 1
12996.2.a.c 1
12996.2.a.d 1
12996.2.a.e 1
12996.2.a.f 1
12996.2.a.g 1
12996.2.a.h 1
12996.2.a.i 1
12996.2.a.j 1
12996.2.a.k 1
12996.2.a.l 1
12996.2.a.m 1
12996.2.a.n 1
12996.2.a.o 1
12996.2.a.p 1
12996.2.a.q 2
12996.2.a.r 2
12996.2.a.s 2
12996.2.a.t 2
12996.2.a.u 2
12996.2.a.v 2
12996.2.a.w 2
12996.2.a.x 2
12996.2.a.y 2
12996.2.a.z 2
12996.2.a.ba 2
12996.2.a.bb 2
12996.2.a.bc 2
12996.2.a.bd 3
12996.2.a.be 3
12996.2.a.bf 3
12996.2.a.bg 3
12996.2.a.bh 4
12996.2.a.bi 4
12996.2.a.bj 4
12996.2.a.bk 4
12996.2.a.bl 4
12996.2.a.bm 4
12996.2.a.bn 4
12996.2.a.bo 6
12996.2.a.bp 6
12996.2.a.bq 6
12996.2.a.br 6
12996.2.a.bs 6
12996.2.a.bt 6
12996.2.a.bu 8
12996.2.a.bv 16
12996.2.c \(\chi_{12996}(12275, \cdot)\) n/a 682 1
12996.2.d \(\chi_{12996}(6497, \cdot)\) n/a 112 1
12996.2.f \(\chi_{12996}(7219, \cdot)\) n/a 834 1
12996.2.i \(\chi_{12996}(4333, \cdot)\) n/a 682 2
12996.2.j \(\chi_{12996}(6205, \cdot)\) n/a 680 2
12996.2.k \(\chi_{12996}(1873, \cdot)\) n/a 282 2
12996.2.l \(\chi_{12996}(3541, \cdot)\) n/a 680 2
12996.2.n \(\chi_{12996}(2957, \cdot)\) n/a 680 2
12996.2.o \(\chi_{12996}(5483, \cdot)\) n/a 4016 2
12996.2.r \(\chi_{12996}(5347, \cdot)\) n/a 1668 2
12996.2.u \(\chi_{12996}(3679, \cdot)\) n/a 4016 2
12996.2.w \(\chi_{12996}(2887, \cdot)\) n/a 4016 2
12996.2.z \(\chi_{12996}(1151, \cdot)\) n/a 1360 2
12996.2.bb \(\chi_{12996}(293, \cdot)\) n/a 680 2
12996.2.bd \(\chi_{12996}(2165, \cdot)\) n/a 680 2
12996.2.bg \(\chi_{12996}(3611, \cdot)\) n/a 4024 2
12996.2.bi \(\chi_{12996}(2819, \cdot)\) n/a 4016 2
12996.2.bk \(\chi_{12996}(4625, \cdot)\) n/a 224 2
12996.2.bn \(\chi_{12996}(1015, \cdot)\) n/a 4016 2
12996.2.bo \(\chi_{12996}(3133, \cdot)\) n/a 852 6
12996.2.bp \(\chi_{12996}(2761, \cdot)\) n/a 2040 6
12996.2.bq \(\chi_{12996}(2581, \cdot)\) n/a 2040 6
12996.2.bs \(\chi_{12996}(2039, \cdot)\) n/a 12048 6
12996.2.bt \(\chi_{12996}(4459, \cdot)\) n/a 12048 6
12996.2.bv \(\chi_{12996}(3737, \cdot)\) n/a 2040 6
12996.2.bz \(\chi_{12996}(2465, \cdot)\) n/a 684 6
12996.2.cc \(\chi_{12996}(4639, \cdot)\) n/a 12048 6
12996.2.ce \(\chi_{12996}(2411, \cdot)\) n/a 4080 6
12996.2.cf \(\chi_{12996}(127, \cdot)\) n/a 5004 6
12996.2.ch \(\chi_{12996}(1859, \cdot)\) n/a 12048 6
12996.2.cl \(\chi_{12996}(3917, \cdot)\) n/a 2040 6
12996.2.cm \(\chi_{12996}(685, \cdot)\) n/a 2862 18
12996.2.cp \(\chi_{12996}(379, \cdot)\) n/a 17064 18
12996.2.cr \(\chi_{12996}(341, \cdot)\) n/a 2304 18
12996.2.cs \(\chi_{12996}(647, \cdot)\) n/a 13680 18
12996.2.cu \(\chi_{12996}(121, \cdot)\) n/a 13680 36
12996.2.cv \(\chi_{12996}(505, \cdot)\) n/a 5724 36
12996.2.cw \(\chi_{12996}(49, \cdot)\) n/a 13680 36
12996.2.cx \(\chi_{12996}(229, \cdot)\) n/a 13680 36
12996.2.cy \(\chi_{12996}(31, \cdot)\) n/a 81936 36
12996.2.db \(\chi_{12996}(449, \cdot)\) n/a 4608 36
12996.2.dd \(\chi_{12996}(83, \cdot)\) n/a 81936 36
12996.2.df \(\chi_{12996}(191, \cdot)\) n/a 81936 36
12996.2.di \(\chi_{12996}(113, \cdot)\) n/a 13680 36
12996.2.dk \(\chi_{12996}(677, \cdot)\) n/a 13680 36
12996.2.dm \(\chi_{12996}(467, \cdot)\) n/a 27360 36
12996.2.dp \(\chi_{12996}(151, \cdot)\) n/a 81936 36
12996.2.dr \(\chi_{12996}(103, \cdot)\) n/a 81936 36
12996.2.du \(\chi_{12996}(487, \cdot)\) n/a 34128 36
12996.2.dx \(\chi_{12996}(11, \cdot)\) n/a 81936 36
12996.2.dy \(\chi_{12996}(65, \cdot)\) n/a 13680 36
12996.2.ea \(\chi_{12996}(85, \cdot)\) n/a 41040 108
12996.2.eb \(\chi_{12996}(25, \cdot)\) n/a 41040 108
12996.2.ec \(\chi_{12996}(73, \cdot)\) n/a 17064 108
12996.2.ed \(\chi_{12996}(173, \cdot)\) n/a 41040 108
12996.2.eh \(\chi_{12996}(47, \cdot)\) n/a 245808 108
12996.2.ej \(\chi_{12996}(91, \cdot)\) n/a 102384 108
12996.2.ek \(\chi_{12996}(35, \cdot)\) n/a 82080 108
12996.2.em \(\chi_{12996}(211, \cdot)\) n/a 245808 108
12996.2.ep \(\chi_{12996}(53, \cdot)\) n/a 13608 108
12996.2.et \(\chi_{12996}(29, \cdot)\) n/a 41040 108
12996.2.ev \(\chi_{12996}(67, \cdot)\) n/a 245808 108
12996.2.ew \(\chi_{12996}(23, \cdot)\) n/a 245808 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(12996))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(12996)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1444))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2166))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3249))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4332))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6498))\)\(^{\oplus 2}\)