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Properties

Label 9747.2
Level 9747
Weight 2
Dimension 2749645
Nonzero newspaces 68
Sturm bound 14035680

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Defining parameters

Level: \( N \) = \( 9747 = 3^{3} \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 68 \)
Sturm bound: \(14035680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9747))\).

Total New Old
Modular forms 3524040 2764637 759403
Cusp forms 3493801 2749645 744156
Eisenstein series 30239 14992 15247

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9747))\)

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
9747.2.a \(\chi_{9747}(1, \cdot)\) 9747.2.a.a 1 1
9747.2.a.b 1
9747.2.a.c 1
9747.2.a.d 1
9747.2.a.e 1
9747.2.a.f 1
9747.2.a.g 1
9747.2.a.h 1
9747.2.a.i 1
9747.2.a.j 1
9747.2.a.k 1
9747.2.a.l 2
9747.2.a.m 2
9747.2.a.n 2
9747.2.a.o 2
9747.2.a.p 2
9747.2.a.q 2
9747.2.a.r 2
9747.2.a.s 2
9747.2.a.t 2
9747.2.a.u 3
9747.2.a.v 3
9747.2.a.w 3
9747.2.a.x 3
9747.2.a.y 3
9747.2.a.z 3
9747.2.a.ba 3
9747.2.a.bb 3
9747.2.a.bc 3
9747.2.a.bd 3
9747.2.a.be 4
9747.2.a.bf 4
9747.2.a.bg 4
9747.2.a.bh 4
9747.2.a.bi 4
9747.2.a.bj 4
9747.2.a.bk 6
9747.2.a.bl 6
9747.2.a.bm 6
9747.2.a.bn 6
9747.2.a.bo 6
9747.2.a.bp 6
9747.2.a.bq 6
9747.2.a.br 6
9747.2.a.bs 6
9747.2.a.bt 6
9747.2.a.bu 12
9747.2.a.bv 12
9747.2.a.bw 12
9747.2.a.bx 12
9747.2.a.by 12
9747.2.a.bz 12
9747.2.a.ca 12
9747.2.a.cb 12
9747.2.a.cc 18
9747.2.a.cd 18
9747.2.a.ce 18
9747.2.a.cf 18
9747.2.a.cg 24
9747.2.a.ch 24
9747.2.a.ci 24
9747.2.a.cj 24
9747.2.a.ck 24
9747.2.a.cl 24
9747.2.d \(\chi_{9747}(9746, \cdot)\) n/a 454 1
9747.2.e \(\chi_{9747}(3250, \cdot)\) n/a 648 2
9747.2.f \(\chi_{9747}(2458, \cdot)\) n/a 908 2
9747.2.g \(\chi_{9747}(5122, \cdot)\) n/a 648 2
9747.2.h \(\chi_{9747}(1873, \cdot)\) n/a 648 2
9747.2.k \(\chi_{9747}(4040, \cdot)\) n/a 648 2
9747.2.l \(\chi_{9747}(3248, \cdot)\) n/a 648 2
9747.2.m \(\chi_{9747}(1376, \cdot)\) n/a 908 2
9747.2.t \(\chi_{9747}(791, \cdot)\) n/a 648 2
9747.2.u \(\chi_{9747}(1498, \cdot)\) n/a 6024 6
9747.2.v \(\chi_{9747}(967, \cdot)\) n/a 6024 6
9747.2.w \(\chi_{9747}(1543, \cdot)\) n/a 6024 6
9747.2.x \(\chi_{9747}(1111, \cdot)\) n/a 6024 6
9747.2.y \(\chi_{9747}(28, \cdot)\) n/a 2718 6
9747.2.z \(\chi_{9747}(415, \cdot)\) n/a 1944 6
9747.2.ba \(\chi_{9747}(1084, \cdot)\) n/a 6036 6
9747.2.bb \(\chi_{9747}(292, \cdot)\) n/a 6024 6
9747.2.bc \(\chi_{9747}(1375, \cdot)\) n/a 6024 6
9747.2.bd \(\chi_{9747}(3277, \cdot)\) n/a 1944 6
9747.2.be \(\chi_{9747}(1678, \cdot)\) n/a 6024 6
9747.2.bf \(\chi_{9747}(1867, \cdot)\) n/a 6024 6
9747.2.bi \(\chi_{9747}(623, \cdot)\) n/a 6024 6
9747.2.bj \(\chi_{9747}(488, \cdot)\) n/a 6024 6
9747.2.bk \(\chi_{9747}(299, \cdot)\) n/a 6024 6
9747.2.bo \(\chi_{9747}(2654, \cdot)\) n/a 1944 6
9747.2.bp \(\chi_{9747}(2834, \cdot)\) n/a 2718 6
9747.2.bu \(\chi_{9747}(293, \cdot)\) n/a 6024 6
9747.2.bv \(\chi_{9747}(2459, \cdot)\) n/a 6024 6
9747.2.bw \(\chi_{9747}(1082, \cdot)\) n/a 6024 6
9747.2.cd \(\chi_{9747}(116, \cdot)\) n/a 1944 6
9747.2.cg \(\chi_{9747}(1571, \cdot)\) n/a 6024 6
9747.2.ch \(\chi_{9747}(1706, \cdot)\) n/a 6024 6
9747.2.cp \(\chi_{9747}(1055, \cdot)\) n/a 6024 6
9747.2.cq \(\chi_{9747}(514, \cdot)\) n/a 9108 18
9747.2.cr \(\chi_{9747}(512, \cdot)\) n/a 9108 18
9747.2.cu \(\chi_{9747}(235, \cdot)\) n/a 13608 36
9747.2.cv \(\chi_{9747}(64, \cdot)\) n/a 13608 36
9747.2.cw \(\chi_{9747}(163, \cdot)\) n/a 18216 36
9747.2.cx \(\chi_{9747}(172, \cdot)\) n/a 13608 36
9747.2.cy \(\chi_{9747}(179, \cdot)\) n/a 13608 36
9747.2.df \(\chi_{9747}(107, \cdot)\) n/a 18216 36
9747.2.dg \(\chi_{9747}(170, \cdot)\) n/a 13608 36
9747.2.dh \(\chi_{9747}(8, \cdot)\) n/a 13608 36
9747.2.dk \(\chi_{9747}(61, \cdot)\) n/a 122904 108
9747.2.dl \(\chi_{9747}(139, \cdot)\) n/a 122904 108
9747.2.dm \(\chi_{9747}(73, \cdot)\) n/a 40824 108
9747.2.dn \(\chi_{9747}(7, \cdot)\) n/a 122904 108
9747.2.do \(\chi_{9747}(106, \cdot)\) n/a 122904 108
9747.2.dp \(\chi_{9747}(58, \cdot)\) n/a 122904 108
9747.2.dq \(\chi_{9747}(226, \cdot)\) n/a 40824 108
9747.2.dr \(\chi_{9747}(55, \cdot)\) n/a 54756 108
9747.2.ds \(\chi_{9747}(43, \cdot)\) n/a 122904 108
9747.2.dt \(\chi_{9747}(4, \cdot)\) n/a 122904 108
9747.2.du \(\chi_{9747}(196, \cdot)\) n/a 122904 108
9747.2.dv \(\chi_{9747}(25, \cdot)\) n/a 122904 108
9747.2.dw \(\chi_{9747}(29, \cdot)\) n/a 122904 108
9747.2.ee \(\chi_{9747}(167, \cdot)\) n/a 122904 108
9747.2.ef \(\chi_{9747}(2, \cdot)\) n/a 122904 108
9747.2.ei \(\chi_{9747}(260, \cdot)\) n/a 40824 108
9747.2.ep \(\chi_{9747}(56, \cdot)\) n/a 122904 108
9747.2.eq \(\chi_{9747}(50, \cdot)\) n/a 122904 108
9747.2.er \(\chi_{9747}(122, \cdot)\) n/a 122904 108
9747.2.ew \(\chi_{9747}(53, \cdot)\) n/a 54756 108
9747.2.ex \(\chi_{9747}(71, \cdot)\) n/a 40824 108
9747.2.fb \(\chi_{9747}(86, \cdot)\) n/a 122904 108
9747.2.fc \(\chi_{9747}(41, \cdot)\) n/a 122904 108
9747.2.fd \(\chi_{9747}(14, \cdot)\) n/a 122904 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9747))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9747)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(513))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3249))\)\(^{\oplus 2}\)