Properties

Label 6776.2
Level 6776
Weight 2
Dimension 736232
Nonzero newspaces 48
Sturm bound 5575680

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Defining parameters

Level: \( N \) = \( 6776 = 2^{3} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(5575680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6776))\).

Total New Old
Modular forms 1405440 741852 663588
Cusp forms 1382401 736232 646169
Eisenstein series 23039 5620 17419

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6776))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6776.2.a \(\chi_{6776}(1, \cdot)\) 6776.2.a.a 1 1
6776.2.a.b 1
6776.2.a.c 1
6776.2.a.d 1
6776.2.a.e 1
6776.2.a.f 1
6776.2.a.g 1
6776.2.a.h 1
6776.2.a.i 1
6776.2.a.j 2
6776.2.a.k 2
6776.2.a.l 2
6776.2.a.m 2
6776.2.a.n 2
6776.2.a.o 2
6776.2.a.p 2
6776.2.a.q 2
6776.2.a.r 2
6776.2.a.s 2
6776.2.a.t 2
6776.2.a.u 3
6776.2.a.v 3
6776.2.a.w 3
6776.2.a.x 3
6776.2.a.y 3
6776.2.a.z 4
6776.2.a.ba 4
6776.2.a.bb 4
6776.2.a.bc 5
6776.2.a.bd 5
6776.2.a.be 6
6776.2.a.bf 6
6776.2.a.bg 6
6776.2.a.bh 6
6776.2.a.bi 8
6776.2.a.bj 8
6776.2.a.bk 8
6776.2.a.bl 8
6776.2.a.bm 10
6776.2.a.bn 10
6776.2.a.bo 10
6776.2.a.bp 10
6776.2.c \(\chi_{6776}(3389, \cdot)\) n/a 654 1
6776.2.e \(\chi_{6776}(5081, \cdot)\) n/a 216 1
6776.2.f \(\chi_{6776}(967, \cdot)\) None 0 1
6776.2.h \(\chi_{6776}(4115, \cdot)\) n/a 854 1
6776.2.j \(\chi_{6776}(727, \cdot)\) None 0 1
6776.2.l \(\chi_{6776}(4355, \cdot)\) n/a 648 1
6776.2.o \(\chi_{6776}(1693, \cdot)\) n/a 848 1
6776.2.q \(\chi_{6776}(3873, \cdot)\) n/a 436 2
6776.2.r \(\chi_{6776}(729, \cdot)\) n/a 648 4
6776.2.s \(\chi_{6776}(3629, \cdot)\) n/a 1696 2
6776.2.w \(\chi_{6776}(2663, \cdot)\) None 0 2
6776.2.y \(\chi_{6776}(1451, \cdot)\) n/a 1696 2
6776.2.ba \(\chi_{6776}(4839, \cdot)\) None 0 2
6776.2.bc \(\chi_{6776}(243, \cdot)\) n/a 1708 2
6776.2.bd \(\chi_{6776}(485, \cdot)\) n/a 1708 2
6776.2.bf \(\chi_{6776}(241, \cdot)\) n/a 432 2
6776.2.bi \(\chi_{6776}(965, \cdot)\) n/a 3392 4
6776.2.bl \(\chi_{6776}(1443, \cdot)\) n/a 2592 4
6776.2.bn \(\chi_{6776}(1455, \cdot)\) None 0 4
6776.2.bp \(\chi_{6776}(27, \cdot)\) n/a 3392 4
6776.2.br \(\chi_{6776}(239, \cdot)\) None 0 4
6776.2.bs \(\chi_{6776}(2169, \cdot)\) n/a 864 4
6776.2.bu \(\chi_{6776}(4117, \cdot)\) n/a 2592 4
6776.2.bw \(\chi_{6776}(617, \cdot)\) n/a 1980 10
6776.2.bx \(\chi_{6776}(9, \cdot)\) n/a 1728 8
6776.2.bz \(\chi_{6776}(419, \cdot)\) n/a 10520 10
6776.2.cb \(\chi_{6776}(351, \cdot)\) None 0 10
6776.2.cc \(\chi_{6776}(153, \cdot)\) n/a 2640 10
6776.2.ce \(\chi_{6776}(309, \cdot)\) n/a 7920 10
6776.2.ch \(\chi_{6776}(461, \cdot)\) n/a 10520 10
6776.2.ck \(\chi_{6776}(43, \cdot)\) n/a 7920 10
6776.2.cm \(\chi_{6776}(111, \cdot)\) None 0 10
6776.2.co \(\chi_{6776}(481, \cdot)\) n/a 1728 8
6776.2.cq \(\chi_{6776}(1213, \cdot)\) n/a 6784 8
6776.2.cr \(\chi_{6776}(3, \cdot)\) n/a 6784 8
6776.2.ct \(\chi_{6776}(1927, \cdot)\) None 0 8
6776.2.cv \(\chi_{6776}(403, \cdot)\) n/a 6784 8
6776.2.cx \(\chi_{6776}(3391, \cdot)\) None 0 8
6776.2.db \(\chi_{6776}(717, \cdot)\) n/a 6784 8
6776.2.dc \(\chi_{6776}(177, \cdot)\) n/a 5280 20
6776.2.dd \(\chi_{6776}(113, \cdot)\) n/a 7920 40
6776.2.de \(\chi_{6776}(219, \cdot)\) n/a 21040 20
6776.2.dg \(\chi_{6776}(199, \cdot)\) None 0 20
6776.2.dk \(\chi_{6776}(285, \cdot)\) n/a 21040 20
6776.2.dm \(\chi_{6776}(593, \cdot)\) n/a 5280 20
6776.2.do \(\chi_{6776}(221, \cdot)\) n/a 21040 20
6776.2.dp \(\chi_{6776}(507, \cdot)\) n/a 21040 20
6776.2.dr \(\chi_{6776}(263, \cdot)\) None 0 20
6776.2.dt \(\chi_{6776}(223, \cdot)\) None 0 40
6776.2.dv \(\chi_{6776}(211, \cdot)\) n/a 31680 40
6776.2.dy \(\chi_{6776}(13, \cdot)\) n/a 42080 40
6776.2.eb \(\chi_{6776}(141, \cdot)\) n/a 31680 40
6776.2.ed \(\chi_{6776}(41, \cdot)\) n/a 10560 40
6776.2.ee \(\chi_{6776}(127, \cdot)\) None 0 40
6776.2.eg \(\chi_{6776}(531, \cdot)\) n/a 42080 40
6776.2.ei \(\chi_{6776}(25, \cdot)\) n/a 21120 80
6776.2.ek \(\chi_{6776}(39, \cdot)\) None 0 80
6776.2.em \(\chi_{6776}(59, \cdot)\) n/a 84160 80
6776.2.en \(\chi_{6776}(37, \cdot)\) n/a 84160 80
6776.2.ep \(\chi_{6776}(17, \cdot)\) n/a 21120 80
6776.2.er \(\chi_{6776}(61, \cdot)\) n/a 84160 80
6776.2.ev \(\chi_{6776}(31, \cdot)\) None 0 80
6776.2.ex \(\chi_{6776}(51, \cdot)\) n/a 84160 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6776))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6776)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1694))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3388))\)\(^{\oplus 2}\)