Properties

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

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

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