Properties

Label 6897.2
Level 6897
Weight 2
Dimension 1273370
Nonzero newspaces 48
Sturm bound 6969600

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Defining parameters

Level: \( N \) = \( 6897 = 3 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(6969600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6897))\).

Total New Old
Modular forms 1753920 1282926 470994
Cusp forms 1730881 1273370 457511
Eisenstein series 23039 9556 13483

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6897))\)

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
6897.2.a \(\chi_{6897}(1, \cdot)\) 6897.2.a.a 1 1
6897.2.a.b 1
6897.2.a.c 1
6897.2.a.d 1
6897.2.a.e 1
6897.2.a.f 1
6897.2.a.g 1
6897.2.a.h 2
6897.2.a.i 2
6897.2.a.j 2
6897.2.a.k 2
6897.2.a.l 3
6897.2.a.m 3
6897.2.a.n 3
6897.2.a.o 3
6897.2.a.p 3
6897.2.a.q 4
6897.2.a.r 5
6897.2.a.s 5
6897.2.a.t 6
6897.2.a.u 6
6897.2.a.v 6
6897.2.a.w 6
6897.2.a.x 6
6897.2.a.y 6
6897.2.a.z 7
6897.2.a.ba 7
6897.2.a.bb 8
6897.2.a.bc 8
6897.2.a.bd 8
6897.2.a.be 8
6897.2.a.bf 12
6897.2.a.bg 12
6897.2.a.bh 14
6897.2.a.bi 14
6897.2.a.bj 14
6897.2.a.bk 14
6897.2.a.bl 16
6897.2.a.bm 16
6897.2.a.bn 20
6897.2.a.bo 20
6897.2.a.bp 24
6897.2.a.bq 24
6897.2.f \(\chi_{6897}(362, \cdot)\) n/a 648 1
6897.2.g \(\chi_{6897}(1937, \cdot)\) n/a 708 1
6897.2.h \(\chi_{6897}(4597, \cdot)\) n/a 360 1
6897.2.i \(\chi_{6897}(1090, \cdot)\) n/a 728 2
6897.2.j \(\chi_{6897}(856, \cdot)\) n/a 1296 4
6897.2.k \(\chi_{6897}(2782, \cdot)\) n/a 720 2
6897.2.l \(\chi_{6897}(1451, \cdot)\) n/a 1408 2
6897.2.m \(\chi_{6897}(122, \cdot)\) n/a 1416 2
6897.2.r \(\chi_{6897}(727, \cdot)\) n/a 2178 6
6897.2.s \(\chi_{6897}(94, \cdot)\) n/a 1440 4
6897.2.t \(\chi_{6897}(2792, \cdot)\) n/a 2816 4
6897.2.u \(\chi_{6897}(2756, \cdot)\) n/a 2592 4
6897.2.z \(\chi_{6897}(628, \cdot)\) n/a 3960 10
6897.2.ba \(\chi_{6897}(1945, \cdot)\) n/a 2880 8
6897.2.bb \(\chi_{6897}(485, \cdot)\) n/a 4254 6
6897.2.be \(\chi_{6897}(1088, \cdot)\) n/a 4224 6
6897.2.bf \(\chi_{6897}(241, \cdot)\) n/a 2160 6
6897.2.bi \(\chi_{6897}(208, \cdot)\) n/a 4400 10
6897.2.bj \(\chi_{6897}(56, \cdot)\) n/a 8760 10
6897.2.bk \(\chi_{6897}(989, \cdot)\) n/a 7920 10
6897.2.bt \(\chi_{6897}(977, \cdot)\) n/a 5632 8
6897.2.bu \(\chi_{6897}(239, \cdot)\) n/a 5632 8
6897.2.bv \(\chi_{6897}(844, \cdot)\) n/a 2880 8
6897.2.bw \(\chi_{6897}(463, \cdot)\) n/a 8800 20
6897.2.bx \(\chi_{6897}(130, \cdot)\) n/a 8640 24
6897.2.by \(\chi_{6897}(58, \cdot)\) n/a 15840 40
6897.2.cd \(\chi_{6897}(221, \cdot)\) n/a 17520 20
6897.2.ce \(\chi_{6897}(197, \cdot)\) n/a 17520 20
6897.2.cf \(\chi_{6897}(274, \cdot)\) n/a 8800 20
6897.2.ci \(\chi_{6897}(40, \cdot)\) n/a 8640 24
6897.2.cj \(\chi_{6897}(161, \cdot)\) n/a 16896 24
6897.2.cm \(\chi_{6897}(269, \cdot)\) n/a 16896 24
6897.2.cn \(\chi_{6897}(100, \cdot)\) n/a 26400 60
6897.2.cs \(\chi_{6897}(134, \cdot)\) n/a 31680 40
6897.2.ct \(\chi_{6897}(113, \cdot)\) n/a 35040 40
6897.2.cu \(\chi_{6897}(151, \cdot)\) n/a 17600 40
6897.2.cv \(\chi_{6897}(49, \cdot)\) n/a 35200 80
6897.2.cy \(\chi_{6897}(10, \cdot)\) n/a 26400 60
6897.2.cz \(\chi_{6897}(131, \cdot)\) n/a 52560 60
6897.2.dc \(\chi_{6897}(89, \cdot)\) n/a 52560 60
6897.2.dd \(\chi_{6897}(46, \cdot)\) n/a 35200 80
6897.2.de \(\chi_{6897}(68, \cdot)\) n/a 70080 80
6897.2.df \(\chi_{6897}(179, \cdot)\) n/a 70080 80
6897.2.dk \(\chi_{6897}(4, \cdot)\) n/a 105600 240
6897.2.dl \(\chi_{6897}(14, \cdot)\) n/a 210240 240
6897.2.do \(\chi_{6897}(17, \cdot)\) n/a 210240 240
6897.2.dp \(\chi_{6897}(13, \cdot)\) n/a 105600 240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6897))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6897)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2299))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6897))\)\(^{\oplus 1}\)