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Properties

Label 12138.2
Level 12138
Weight 2
Dimension 950558
Nonzero newspaces 40
Sturm bound 15980544

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Defining parameters

Level: \( N \) = \( 12138 = 2 \cdot 3 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(15980544\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(12138))\).

Total New Old
Modular forms 4014336 950558 3063778
Cusp forms 3975937 950558 3025379
Eisenstein series 38399 0 38399

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(12138))\)

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
12138.2.a \(\chi_{12138}(1, \cdot)\) 12138.2.a.a 1 1
12138.2.a.b 1
12138.2.a.c 1
12138.2.a.d 1
12138.2.a.e 1
12138.2.a.f 1
12138.2.a.g 1
12138.2.a.h 1
12138.2.a.i 1
12138.2.a.j 1
12138.2.a.k 1
12138.2.a.l 1
12138.2.a.m 1
12138.2.a.n 1
12138.2.a.o 1
12138.2.a.p 1
12138.2.a.q 1
12138.2.a.r 1
12138.2.a.s 1
12138.2.a.t 1
12138.2.a.u 1
12138.2.a.v 1
12138.2.a.w 1
12138.2.a.x 1
12138.2.a.y 1
12138.2.a.z 1
12138.2.a.ba 1
12138.2.a.bb 1
12138.2.a.bc 1
12138.2.a.bd 1
12138.2.a.be 2
12138.2.a.bf 2
12138.2.a.bg 2
12138.2.a.bh 2
12138.2.a.bi 2
12138.2.a.bj 2
12138.2.a.bk 2
12138.2.a.bl 2
12138.2.a.bm 2
12138.2.a.bn 2
12138.2.a.bo 2
12138.2.a.bp 2
12138.2.a.bq 2
12138.2.a.br 2
12138.2.a.bs 2
12138.2.a.bt 2
12138.2.a.bu 2
12138.2.a.bv 2
12138.2.a.bw 2
12138.2.a.bx 2
12138.2.a.by 4
12138.2.a.bz 4
12138.2.a.ca 4
12138.2.a.cb 4
12138.2.a.cc 4
12138.2.a.cd 4
12138.2.a.ce 6
12138.2.a.cf 6
12138.2.a.cg 6
12138.2.a.ch 6
12138.2.a.ci 6
12138.2.a.cj 6
12138.2.a.ck 6
12138.2.a.cl 6
12138.2.a.cm 6
12138.2.a.cn 6
12138.2.a.co 6
12138.2.a.cp 6
12138.2.a.cq 6
12138.2.a.cr 6
12138.2.a.cs 6
12138.2.a.ct 6
12138.2.a.cu 6
12138.2.a.cv 6
12138.2.a.cw 6
12138.2.a.cx 6
12138.2.a.cy 8
12138.2.a.cz 8
12138.2.a.da 8
12138.2.a.db 8
12138.2.a.dc 12
12138.2.a.dd 12
12138.2.b \(\chi_{12138}(2311, \cdot)\) n/a 268 1
12138.2.e \(\chi_{12138}(12137, \cdot)\) n/a 720 1
12138.2.f \(\chi_{12138}(9827, \cdot)\) n/a 724 1
12138.2.i \(\chi_{12138}(3469, \cdot)\) n/a 724 2
12138.2.k \(\chi_{12138}(251, \cdot)\) n/a 1440 2
12138.2.m \(\chi_{12138}(2563, \cdot)\) n/a 536 2
12138.2.p \(\chi_{12138}(4625, \cdot)\) n/a 1444 2
12138.2.q \(\chi_{12138}(6935, \cdot)\) n/a 1440 2
12138.2.t \(\chi_{12138}(5779, \cdot)\) n/a 720 2
12138.2.u \(\chi_{12138}(757, \cdot)\) n/a 1088 4
12138.2.w \(\chi_{12138}(1889, \cdot)\) n/a 2880 4
12138.2.y \(\chi_{12138}(4373, \cdot)\) n/a 2880 4
12138.2.ba \(\chi_{12138}(3217, \cdot)\) n/a 1440 4
12138.2.be \(\chi_{12138}(643, \cdot)\) n/a 2880 8
12138.2.bf \(\chi_{12138}(827, \cdot)\) n/a 4320 8
12138.2.bg \(\chi_{12138}(715, \cdot)\) n/a 4928 16
12138.2.bi \(\chi_{12138}(1579, \cdot)\) n/a 2880 8
12138.2.bk \(\chi_{12138}(2735, \cdot)\) n/a 5760 8
12138.2.bn \(\chi_{12138}(545, \cdot)\) n/a 13056 16
12138.2.bo \(\chi_{12138}(713, \cdot)\) n/a 13056 16
12138.2.br \(\chi_{12138}(169, \cdot)\) n/a 4928 16
12138.2.bs \(\chi_{12138}(65, \cdot)\) n/a 11520 16
12138.2.bt \(\chi_{12138}(1081, \cdot)\) n/a 5760 16
12138.2.bw \(\chi_{12138}(205, \cdot)\) n/a 13056 32
12138.2.bx \(\chi_{12138}(421, \cdot)\) n/a 9856 32
12138.2.bz \(\chi_{12138}(293, \cdot)\) n/a 26112 32
12138.2.cb \(\chi_{12138}(67, \cdot)\) n/a 13056 32
12138.2.ce \(\chi_{12138}(101, \cdot)\) n/a 26112 32
12138.2.cf \(\chi_{12138}(341, \cdot)\) n/a 26112 32
12138.2.cj \(\chi_{12138}(83, \cdot)\) n/a 52224 64
12138.2.cl \(\chi_{12138}(43, \cdot)\) n/a 19456 64
12138.2.cn \(\chi_{12138}(319, \cdot)\) n/a 26112 64
12138.2.cp \(\chi_{12138}(47, \cdot)\) n/a 52224 64
12138.2.cq \(\chi_{12138}(29, \cdot)\) n/a 78336 128
12138.2.cr \(\chi_{12138}(97, \cdot)\) n/a 52224 128
12138.2.cu \(\chi_{12138}(59, \cdot)\) n/a 104448 128
12138.2.cw \(\chi_{12138}(25, \cdot)\) n/a 52224 128
12138.2.da \(\chi_{12138}(31, \cdot)\) n/a 104448 256
12138.2.db \(\chi_{12138}(11, \cdot)\) n/a 208896 256

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(12138))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(12138)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(714))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1734))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2023))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4046))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6069))\)\(^{\oplus 2}\)