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Properties

Label 6760.2
Level 6760
Weight 2
Dimension 691957
Nonzero newspaces 64
Sturm bound 5451264

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Defining parameters

Level: \( N \) = \( 6760 = 2^{3} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(5451264\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6760))\).

Total New Old
Modular forms 1373760 696865 676895
Cusp forms 1351873 691957 659916
Eisenstein series 21887 4908 16979

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6760))\)

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
6760.2.a \(\chi_{6760}(1, \cdot)\) 6760.2.a.a 1 1
6760.2.a.b 1
6760.2.a.c 1
6760.2.a.d 1
6760.2.a.e 1
6760.2.a.f 1
6760.2.a.g 1
6760.2.a.h 1
6760.2.a.i 1
6760.2.a.j 1
6760.2.a.k 1
6760.2.a.l 1
6760.2.a.m 1
6760.2.a.n 2
6760.2.a.o 2
6760.2.a.p 2
6760.2.a.q 2
6760.2.a.r 2
6760.2.a.s 2
6760.2.a.t 2
6760.2.a.u 3
6760.2.a.v 3
6760.2.a.w 3
6760.2.a.x 3
6760.2.a.y 3
6760.2.a.z 3
6760.2.a.ba 4
6760.2.a.bb 4
6760.2.a.bc 4
6760.2.a.bd 4
6760.2.a.be 6
6760.2.a.bf 6
6760.2.a.bg 6
6760.2.a.bh 6
6760.2.a.bi 6
6760.2.a.bj 6
6760.2.a.bk 8
6760.2.a.bl 8
6760.2.a.bm 9
6760.2.a.bn 9
6760.2.a.bo 12
6760.2.a.bp 12
6760.2.d \(\chi_{6760}(5409, \cdot)\) n/a 232 1
6760.2.e \(\chi_{6760}(6421, \cdot)\) n/a 616 1
6760.2.f \(\chi_{6760}(1689, \cdot)\) n/a 232 1
6760.2.g \(\chi_{6760}(3381, \cdot)\) n/a 620 1
6760.2.j \(\chi_{6760}(2029, \cdot)\) n/a 908 1
6760.2.k \(\chi_{6760}(3041, \cdot)\) n/a 154 1
6760.2.p \(\chi_{6760}(5069, \cdot)\) n/a 904 1
6760.2.q \(\chi_{6760}(1881, \cdot)\) n/a 308 2
6760.2.s \(\chi_{6760}(1591, \cdot)\) None 0 2
6760.2.t \(\chi_{6760}(99, \cdot)\) n/a 1808 2
6760.2.w \(\chi_{6760}(577, \cdot)\) n/a 462 2
6760.2.y \(\chi_{6760}(3957, \cdot)\) n/a 1808 2
6760.2.bb \(\chi_{6760}(2367, \cdot)\) None 0 2
6760.2.bc \(\chi_{6760}(2027, \cdot)\) n/a 1808 2
6760.2.bd \(\chi_{6760}(2703, \cdot)\) None 0 2
6760.2.be \(\chi_{6760}(3043, \cdot)\) n/a 1816 2
6760.2.bh \(\chi_{6760}(3817, \cdot)\) n/a 462 2
6760.2.bj \(\chi_{6760}(437, \cdot)\) n/a 1808 2
6760.2.bm \(\chi_{6760}(1451, \cdot)\) n/a 1232 2
6760.2.bn \(\chi_{6760}(239, \cdot)\) None 0 2
6760.2.bp \(\chi_{6760}(2389, \cdot)\) n/a 1808 2
6760.2.bu \(\chi_{6760}(361, \cdot)\) n/a 308 2
6760.2.bv \(\chi_{6760}(3909, \cdot)\) n/a 1808 2
6760.2.by \(\chi_{6760}(5261, \cdot)\) n/a 1232 2
6760.2.bz \(\chi_{6760}(5769, \cdot)\) n/a 464 2
6760.2.ca \(\chi_{6760}(3741, \cdot)\) n/a 1232 2
6760.2.cb \(\chi_{6760}(529, \cdot)\) n/a 460 2
6760.2.cf \(\chi_{6760}(319, \cdot)\) None 0 4
6760.2.cg \(\chi_{6760}(1371, \cdot)\) n/a 2464 4
6760.2.cj \(\chi_{6760}(2117, \cdot)\) n/a 3616 4
6760.2.cl \(\chi_{6760}(657, \cdot)\) n/a 924 4
6760.2.cm \(\chi_{6760}(867, \cdot)\) n/a 3616 4
6760.2.cn \(\chi_{6760}(23, \cdot)\) None 0 4
6760.2.cs \(\chi_{6760}(147, \cdot)\) n/a 3616 4
6760.2.ct \(\chi_{6760}(1543, \cdot)\) None 0 4
6760.2.cu \(\chi_{6760}(357, \cdot)\) n/a 3616 4
6760.2.cw \(\chi_{6760}(2793, \cdot)\) n/a 924 4
6760.2.cz \(\chi_{6760}(19, \cdot)\) n/a 3616 4
6760.2.da \(\chi_{6760}(1671, \cdot)\) None 0 4
6760.2.dc \(\chi_{6760}(521, \cdot)\) n/a 2184 12
6760.2.dd \(\chi_{6760}(389, \cdot)\) n/a 13056 12
6760.2.di \(\chi_{6760}(441, \cdot)\) n/a 2184 12
6760.2.dj \(\chi_{6760}(469, \cdot)\) n/a 13056 12
6760.2.dm \(\chi_{6760}(261, \cdot)\) n/a 8736 12
6760.2.dn \(\chi_{6760}(129, \cdot)\) n/a 3264 12
6760.2.do \(\chi_{6760}(181, \cdot)\) n/a 8736 12
6760.2.dp \(\chi_{6760}(209, \cdot)\) n/a 3288 12
6760.2.ds \(\chi_{6760}(81, \cdot)\) n/a 4368 24
6760.2.dt \(\chi_{6760}(359, \cdot)\) None 0 24
6760.2.dw \(\chi_{6760}(291, \cdot)\) n/a 17472 24
6760.2.dy \(\chi_{6760}(213, \cdot)\) n/a 26112 24
6760.2.ea \(\chi_{6760}(177, \cdot)\) n/a 6552 24
6760.2.ed \(\chi_{6760}(27, \cdot)\) n/a 26112 24
6760.2.ee \(\chi_{6760}(103, \cdot)\) None 0 24
6760.2.ef \(\chi_{6760}(363, \cdot)\) n/a 26112 24
6760.2.eg \(\chi_{6760}(183, \cdot)\) None 0 24
6760.2.ej \(\chi_{6760}(317, \cdot)\) n/a 26112 24
6760.2.el \(\chi_{6760}(57, \cdot)\) n/a 6552 24
6760.2.en \(\chi_{6760}(499, \cdot)\) n/a 26112 24
6760.2.eq \(\chi_{6760}(31, \cdot)\) None 0 24
6760.2.et \(\chi_{6760}(9, \cdot)\) n/a 6576 24
6760.2.eu \(\chi_{6760}(101, \cdot)\) n/a 17472 24
6760.2.ev \(\chi_{6760}(49, \cdot)\) n/a 6528 24
6760.2.ew \(\chi_{6760}(61, \cdot)\) n/a 17472 24
6760.2.ez \(\chi_{6760}(29, \cdot)\) n/a 26112 24
6760.2.fa \(\chi_{6760}(121, \cdot)\) n/a 4368 24
6760.2.ff \(\chi_{6760}(69, \cdot)\) n/a 26112 24
6760.2.fg \(\chi_{6760}(71, \cdot)\) None 0 48
6760.2.fj \(\chi_{6760}(59, \cdot)\) n/a 52224 48
6760.2.fl \(\chi_{6760}(33, \cdot)\) n/a 13104 48
6760.2.fn \(\chi_{6760}(197, \cdot)\) n/a 52224 48
6760.2.fo \(\chi_{6760}(87, \cdot)\) None 0 48
6760.2.fp \(\chi_{6760}(43, \cdot)\) n/a 52224 48
6760.2.fu \(\chi_{6760}(127, \cdot)\) None 0 48
6760.2.fv \(\chi_{6760}(3, \cdot)\) n/a 52224 48
6760.2.fw \(\chi_{6760}(137, \cdot)\) n/a 13104 48
6760.2.fy \(\chi_{6760}(37, \cdot)\) n/a 52224 48
6760.2.ga \(\chi_{6760}(11, \cdot)\) n/a 34944 48
6760.2.gd \(\chi_{6760}(119, \cdot)\) None 0 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6760)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1690))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3380))\)\(^{\oplus 2}\)