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Properties

Label 9126.2
Level 9126
Weight 2
Dimension 598550
Nonzero newspaces 48
Sturm bound 9199008

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Defining parameters

Level: \( N \) = \( 9126 = 2 \cdot 3^{3} \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(9199008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9126))\).

Total New Old
Modular forms 2313432 598550 1714882
Cusp forms 2286073 598550 1687523
Eisenstein series 27359 0 27359

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9126))\)

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
9126.2.a \(\chi_{9126}(1, \cdot)\) 9126.2.a.a 1 1
9126.2.a.b 1
9126.2.a.c 1
9126.2.a.d 1
9126.2.a.e 1
9126.2.a.f 1
9126.2.a.g 1
9126.2.a.h 1
9126.2.a.i 1
9126.2.a.j 1
9126.2.a.k 1
9126.2.a.l 1
9126.2.a.m 1
9126.2.a.n 1
9126.2.a.o 1
9126.2.a.p 1
9126.2.a.q 1
9126.2.a.r 1
9126.2.a.s 1
9126.2.a.t 1
9126.2.a.u 1
9126.2.a.v 1
9126.2.a.w 1
9126.2.a.x 1
9126.2.a.y 1
9126.2.a.z 1
9126.2.a.ba 1
9126.2.a.bb 1
9126.2.a.bc 1
9126.2.a.bd 1
9126.2.a.be 1
9126.2.a.bf 1
9126.2.a.bg 1
9126.2.a.bh 1
9126.2.a.bi 1
9126.2.a.bj 1
9126.2.a.bk 1
9126.2.a.bl 1
9126.2.a.bm 2
9126.2.a.bn 2
9126.2.a.bo 2
9126.2.a.bp 2
9126.2.a.bq 2
9126.2.a.br 2
9126.2.a.bs 2
9126.2.a.bt 2
9126.2.a.bu 2
9126.2.a.bv 2
9126.2.a.bw 2
9126.2.a.bx 2
9126.2.a.by 2
9126.2.a.bz 2
9126.2.a.ca 2
9126.2.a.cb 2
9126.2.a.cc 2
9126.2.a.cd 2
9126.2.a.ce 3
9126.2.a.cf 3
9126.2.a.cg 3
9126.2.a.ch 3
9126.2.a.ci 4
9126.2.a.cj 4
9126.2.a.ck 4
9126.2.a.cl 4
9126.2.a.cm 4
9126.2.a.cn 4
9126.2.a.co 6
9126.2.a.cp 6
9126.2.a.cq 6
9126.2.a.cr 6
9126.2.a.cs 6
9126.2.a.ct 6
9126.2.a.cu 6
9126.2.a.cv 6
9126.2.a.cw 6
9126.2.a.cx 6
9126.2.a.cy 9
9126.2.a.cz 9
9126.2.a.da 9
9126.2.a.db 9
9126.2.b \(\chi_{9126}(1351, \cdot)\) n/a 204 1
9126.2.e \(\chi_{9126}(3043, \cdot)\) n/a 310 2
9126.2.f \(\chi_{9126}(991, \cdot)\) n/a 308 2
9126.2.g \(\chi_{9126}(2557, \cdot)\) n/a 308 2
9126.2.h \(\chi_{9126}(7075, \cdot)\) n/a 412 2
9126.2.j \(\chi_{9126}(2267, \cdot)\) n/a 408 2
9126.2.l \(\chi_{9126}(1837, \cdot)\) n/a 412 2
9126.2.p \(\chi_{9126}(361, \cdot)\) n/a 308 2
9126.2.s \(\chi_{9126}(6445, \cdot)\) n/a 308 2
9126.2.t \(\chi_{9126}(4393, \cdot)\) n/a 308 2
9126.2.w \(\chi_{9126}(1015, \cdot)\) n/a 2790 6
9126.2.x \(\chi_{9126}(529, \cdot)\) n/a 2772 6
9126.2.y \(\chi_{9126}(1543, \cdot)\) n/a 2772 6
9126.2.ba \(\chi_{9126}(3023, \cdot)\) n/a 824 4
9126.2.bb \(\chi_{9126}(89, \cdot)\) n/a 616 4
9126.2.bc \(\chi_{9126}(1709, \cdot)\) n/a 616 4
9126.2.bg \(\chi_{9126}(2465, \cdot)\) n/a 616 4
9126.2.bh \(\chi_{9126}(703, \cdot)\) n/a 2928 12
9126.2.bk \(\chi_{9126}(2389, \cdot)\) n/a 2772 6
9126.2.bl \(\chi_{9126}(337, \cdot)\) n/a 2772 6
9126.2.bq \(\chi_{9126}(823, \cdot)\) n/a 2772 6
9126.2.bt \(\chi_{9126}(649, \cdot)\) n/a 2928 12
9126.2.bv \(\chi_{9126}(695, \cdot)\) n/a 5544 12
9126.2.bw \(\chi_{9126}(239, \cdot)\) n/a 5544 12
9126.2.bz \(\chi_{9126}(587, \cdot)\) n/a 5544 12
9126.2.ca \(\chi_{9126}(55, \cdot)\) n/a 5808 24
9126.2.cb \(\chi_{9126}(451, \cdot)\) n/a 4368 24
9126.2.cc \(\chi_{9126}(289, \cdot)\) n/a 4368 24
9126.2.cd \(\chi_{9126}(235, \cdot)\) n/a 4368 24
9126.2.ce \(\chi_{9126}(161, \cdot)\) n/a 5856 24
9126.2.ci \(\chi_{9126}(181, \cdot)\) n/a 4368 24
9126.2.cj \(\chi_{9126}(127, \cdot)\) n/a 4368 24
9126.2.cm \(\chi_{9126}(667, \cdot)\) n/a 4368 24
9126.2.cq \(\chi_{9126}(433, \cdot)\) n/a 5808 24
9126.2.cs \(\chi_{9126}(133, \cdot)\) n/a 39312 72
9126.2.ct \(\chi_{9126}(79, \cdot)\) n/a 39312 72
9126.2.cu \(\chi_{9126}(61, \cdot)\) n/a 39312 72
9126.2.cv \(\chi_{9126}(125, \cdot)\) n/a 8736 48
9126.2.cz \(\chi_{9126}(71, \cdot)\) n/a 8736 48
9126.2.da \(\chi_{9126}(215, \cdot)\) n/a 11616 48
9126.2.db \(\chi_{9126}(305, \cdot)\) n/a 8736 48
9126.2.dd \(\chi_{9126}(121, \cdot)\) n/a 39312 72
9126.2.di \(\chi_{9126}(43, \cdot)\) n/a 39312 72
9126.2.dj \(\chi_{9126}(25, \cdot)\) n/a 39312 72
9126.2.dm \(\chi_{9126}(11, \cdot)\) n/a 78624 144
9126.2.dp \(\chi_{9126}(5, \cdot)\) n/a 78624 144
9126.2.dq \(\chi_{9126}(41, \cdot)\) n/a 78624 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9126))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9126)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(702))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1521))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3042))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4563))\)\(^{\oplus 2}\)