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Properties

Label 6768.2
Level 6768
Weight 2
Dimension 564017
Nonzero newspaces 32
Sturm bound 5087232

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Defining parameters

Level: \( N \) = \( 6768 = 2^{4} \cdot 3^{2} \cdot 47 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(5087232\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6768))\).

Total New Old
Modular forms 1282112 567661 714451
Cusp forms 1261505 564017 697488
Eisenstein series 20607 3644 16963

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6768))\)

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
6768.2.a \(\chi_{6768}(1, \cdot)\) 6768.2.a.a 1 1
6768.2.a.b 1
6768.2.a.c 1
6768.2.a.d 1
6768.2.a.e 1
6768.2.a.f 1
6768.2.a.g 1
6768.2.a.h 1
6768.2.a.i 1
6768.2.a.j 1
6768.2.a.k 1
6768.2.a.l 1
6768.2.a.m 1
6768.2.a.n 1
6768.2.a.o 1
6768.2.a.p 1
6768.2.a.q 1
6768.2.a.r 1
6768.2.a.s 1
6768.2.a.t 1
6768.2.a.u 1
6768.2.a.v 2
6768.2.a.w 2
6768.2.a.x 2
6768.2.a.y 2
6768.2.a.z 2
6768.2.a.ba 2
6768.2.a.bb 2
6768.2.a.bc 2
6768.2.a.bd 2
6768.2.a.be 2
6768.2.a.bf 2
6768.2.a.bg 2
6768.2.a.bh 2
6768.2.a.bi 2
6768.2.a.bj 3
6768.2.a.bk 3
6768.2.a.bl 3
6768.2.a.bm 3
6768.2.a.bn 3
6768.2.a.bo 3
6768.2.a.bp 3
6768.2.a.bq 4
6768.2.a.br 4
6768.2.a.bs 4
6768.2.a.bt 4
6768.2.a.bu 4
6768.2.a.bv 4
6768.2.a.bw 5
6768.2.a.bx 8
6768.2.a.by 8
6768.2.c \(\chi_{6768}(3007, \cdot)\) n/a 120 1
6768.2.e \(\chi_{6768}(4607, \cdot)\) 6768.2.e.a 2 1
6768.2.e.b 2
6768.2.e.c 2
6768.2.e.d 2
6768.2.e.e 4
6768.2.e.f 4
6768.2.e.g 4
6768.2.e.h 4
6768.2.e.i 6
6768.2.e.j 6
6768.2.e.k 28
6768.2.e.l 28
6768.2.g \(\chi_{6768}(3385, \cdot)\) None 0 1
6768.2.i \(\chi_{6768}(2537, \cdot)\) None 0 1
6768.2.k \(\chi_{6768}(1223, \cdot)\) None 0 1
6768.2.m \(\chi_{6768}(6391, \cdot)\) None 0 1
6768.2.o \(\chi_{6768}(5921, \cdot)\) 6768.2.o.a 4 1
6768.2.o.b 4
6768.2.o.c 8
6768.2.o.d 16
6768.2.o.e 16
6768.2.o.f 48
6768.2.q \(\chi_{6768}(2257, \cdot)\) n/a 552 2
6768.2.r \(\chi_{6768}(845, \cdot)\) n/a 768 2
6768.2.t \(\chi_{6768}(1693, \cdot)\) n/a 920 2
6768.2.v \(\chi_{6768}(2915, \cdot)\) n/a 736 2
6768.2.x \(\chi_{6768}(1315, \cdot)\) n/a 956 2
6768.2.ba \(\chi_{6768}(1409, \cdot)\) n/a 572 2
6768.2.bc \(\chi_{6768}(1879, \cdot)\) None 0 2
6768.2.be \(\chi_{6768}(3479, \cdot)\) None 0 2
6768.2.bg \(\chi_{6768}(281, \cdot)\) None 0 2
6768.2.bi \(\chi_{6768}(1129, \cdot)\) None 0 2
6768.2.bk \(\chi_{6768}(95, \cdot)\) n/a 552 2
6768.2.bm \(\chi_{6768}(751, \cdot)\) n/a 576 2
6768.2.bp \(\chi_{6768}(659, \cdot)\) n/a 4416 4
6768.2.br \(\chi_{6768}(187, \cdot)\) n/a 4592 4
6768.2.bt \(\chi_{6768}(1973, \cdot)\) n/a 4592 4
6768.2.bv \(\chi_{6768}(565, \cdot)\) n/a 4416 4
6768.2.bw \(\chi_{6768}(145, \cdot)\) n/a 2618 22
6768.2.by \(\chi_{6768}(161, \cdot)\) n/a 2112 22
6768.2.ca \(\chi_{6768}(199, \cdot)\) None 0 22
6768.2.cc \(\chi_{6768}(71, \cdot)\) None 0 22
6768.2.ce \(\chi_{6768}(233, \cdot)\) None 0 22
6768.2.cg \(\chi_{6768}(361, \cdot)\) None 0 22
6768.2.ci \(\chi_{6768}(143, \cdot)\) n/a 2112 22
6768.2.ck \(\chi_{6768}(127, \cdot)\) n/a 2640 22
6768.2.cm \(\chi_{6768}(49, \cdot)\) n/a 12584 44
6768.2.co \(\chi_{6768}(19, \cdot)\) n/a 21032 44
6768.2.cq \(\chi_{6768}(251, \cdot)\) n/a 16896 44
6768.2.cs \(\chi_{6768}(37, \cdot)\) n/a 21032 44
6768.2.cu \(\chi_{6768}(125, \cdot)\) n/a 16896 44
6768.2.cw \(\chi_{6768}(31, \cdot)\) n/a 12672 44
6768.2.cy \(\chi_{6768}(191, \cdot)\) n/a 12672 44
6768.2.da \(\chi_{6768}(25, \cdot)\) None 0 44
6768.2.dc \(\chi_{6768}(41, \cdot)\) None 0 44
6768.2.de \(\chi_{6768}(119, \cdot)\) None 0 44
6768.2.dg \(\chi_{6768}(151, \cdot)\) None 0 44
6768.2.di \(\chi_{6768}(113, \cdot)\) n/a 12584 44
6768.2.dk \(\chi_{6768}(61, \cdot)\) n/a 101024 88
6768.2.dm \(\chi_{6768}(5, \cdot)\) n/a 101024 88
6768.2.do \(\chi_{6768}(43, \cdot)\) n/a 101024 88
6768.2.dq \(\chi_{6768}(59, \cdot)\) n/a 101024 88

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6768))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6768)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(94))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(188))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(282))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(376))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(423))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(564))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(752))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(846))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1692))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3384))\)\(^{\oplus 2}\)