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Properties

Label 6912.2
Level 6912
Weight 2
Dimension 588160
Nonzero newspaces 36
Sturm bound 5308416

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Defining parameters

Level: \( N \) = \( 6912 = 2^{8} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(5308416\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6912))\).

Total New Old
Modular forms 1337664 591488 746176
Cusp forms 1316545 588160 728385
Eisenstein series 21119 3328 17791

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6912))\)

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
6912.2.a \(\chi_{6912}(1, \cdot)\) 6912.2.a.a 1 1
6912.2.a.b 1
6912.2.a.c 1
6912.2.a.d 1
6912.2.a.e 1
6912.2.a.f 1
6912.2.a.g 1
6912.2.a.h 1
6912.2.a.i 1
6912.2.a.j 1
6912.2.a.k 1
6912.2.a.l 1
6912.2.a.m 1
6912.2.a.n 1
6912.2.a.o 1
6912.2.a.p 1
6912.2.a.q 1
6912.2.a.r 1
6912.2.a.s 1
6912.2.a.t 1
6912.2.a.u 1
6912.2.a.v 1
6912.2.a.w 1
6912.2.a.x 1
6912.2.a.y 2
6912.2.a.z 2
6912.2.a.ba 2
6912.2.a.bb 2
6912.2.a.bc 2
6912.2.a.bd 2
6912.2.a.be 2
6912.2.a.bf 2
6912.2.a.bg 2
6912.2.a.bh 2
6912.2.a.bi 2
6912.2.a.bj 2
6912.2.a.bk 2
6912.2.a.bl 2
6912.2.a.bm 2
6912.2.a.bn 2
6912.2.a.bo 2
6912.2.a.bp 2
6912.2.a.bq 2
6912.2.a.br 2
6912.2.a.bs 2
6912.2.a.bt 2
6912.2.a.bu 2
6912.2.a.bv 2
6912.2.a.bw 2
6912.2.a.bx 2
6912.2.a.by 2
6912.2.a.bz 2
6912.2.a.ca 4
6912.2.a.cb 4
6912.2.a.cc 4
6912.2.a.cd 4
6912.2.a.ce 4
6912.2.a.cf 4
6912.2.a.cg 4
6912.2.a.ch 4
6912.2.a.ci 4
6912.2.a.cj 4
6912.2.a.ck 4
6912.2.a.cl 4
6912.2.c \(\chi_{6912}(6911, \cdot)\) n/a 128 1
6912.2.d \(\chi_{6912}(3457, \cdot)\) n/a 128 1
6912.2.f \(\chi_{6912}(3455, \cdot)\) n/a 128 1
6912.2.i \(\chi_{6912}(2305, \cdot)\) n/a 184 2
6912.2.k \(\chi_{6912}(1729, \cdot)\) n/a 256 2
6912.2.l \(\chi_{6912}(1727, \cdot)\) n/a 256 2
6912.2.p \(\chi_{6912}(1151, \cdot)\) n/a 184 2
6912.2.r \(\chi_{6912}(1153, \cdot)\) n/a 184 2
6912.2.s \(\chi_{6912}(2303, \cdot)\) n/a 184 2
6912.2.v \(\chi_{6912}(865, \cdot)\) n/a 512 4
6912.2.w \(\chi_{6912}(863, \cdot)\) n/a 512 4
6912.2.y \(\chi_{6912}(769, \cdot)\) n/a 1704 6
6912.2.z \(\chi_{6912}(575, \cdot)\) n/a 384 4
6912.2.bc \(\chi_{6912}(577, \cdot)\) n/a 384 4
6912.2.be \(\chi_{6912}(433, \cdot)\) n/a 1024 8
6912.2.bf \(\chi_{6912}(431, \cdot)\) n/a 1024 8
6912.2.bj \(\chi_{6912}(385, \cdot)\) n/a 1704 6
6912.2.bl \(\chi_{6912}(383, \cdot)\) n/a 1704 6
6912.2.bm \(\chi_{6912}(767, \cdot)\) n/a 1704 6
6912.2.bo \(\chi_{6912}(289, \cdot)\) n/a 736 8
6912.2.br \(\chi_{6912}(287, \cdot)\) n/a 736 8
6912.2.bt \(\chi_{6912}(217, \cdot)\) None 0 16
6912.2.bu \(\chi_{6912}(215, \cdot)\) None 0 16
6912.2.bw \(\chi_{6912}(193, \cdot)\) n/a 3456 12
6912.2.bz \(\chi_{6912}(191, \cdot)\) n/a 3456 12
6912.2.cb \(\chi_{6912}(143, \cdot)\) n/a 1504 16
6912.2.cc \(\chi_{6912}(145, \cdot)\) n/a 1504 16
6912.2.cf \(\chi_{6912}(109, \cdot)\) n/a 16384 32
6912.2.cg \(\chi_{6912}(107, \cdot)\) n/a 16384 32
6912.2.cj \(\chi_{6912}(95, \cdot)\) n/a 6816 24
6912.2.ck \(\chi_{6912}(97, \cdot)\) n/a 6816 24
6912.2.cm \(\chi_{6912}(71, \cdot)\) None 0 32
6912.2.cp \(\chi_{6912}(73, \cdot)\) None 0 32
6912.2.cq \(\chi_{6912}(49, \cdot)\) n/a 13728 48
6912.2.ct \(\chi_{6912}(47, \cdot)\) n/a 13728 48
6912.2.cu \(\chi_{6912}(37, \cdot)\) n/a 24448 64
6912.2.cx \(\chi_{6912}(35, \cdot)\) n/a 24448 64
6912.2.cz \(\chi_{6912}(25, \cdot)\) None 0 96
6912.2.da \(\chi_{6912}(23, \cdot)\) None 0 96
6912.2.dc \(\chi_{6912}(11, \cdot)\) n/a 220800 192
6912.2.df \(\chi_{6912}(13, \cdot)\) n/a 220800 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6912))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6912)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(864))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1728))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3456))\)\(^{\oplus 2}\)