# Properties

 Label 6498.2 Level 6498 Weight 2 Dimension 306947 Nonzero newspaces 32 Sturm bound 4678560

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## Defining parameters

 Level: $$N$$ = $$6498 = 2 \cdot 3^{2} \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$4678560$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6498))$$.

Total New Old
Modular forms 1177704 306947 870757
Cusp forms 1161577 306947 854630
Eisenstein series 16127 0 16127

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6498))$$

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
6498.2.a $$\chi_{6498}(1, \cdot)$$ 6498.2.a.a 1 1
6498.2.a.b 1
6498.2.a.c 1
6498.2.a.d 1
6498.2.a.e 1
6498.2.a.f 1
6498.2.a.g 1
6498.2.a.h 1
6498.2.a.i 1
6498.2.a.j 1
6498.2.a.k 1
6498.2.a.l 1
6498.2.a.m 1
6498.2.a.n 1
6498.2.a.o 1
6498.2.a.p 1
6498.2.a.q 1
6498.2.a.r 1
6498.2.a.s 1
6498.2.a.t 1
6498.2.a.u 1
6498.2.a.v 1
6498.2.a.w 1
6498.2.a.x 1
6498.2.a.y 1
6498.2.a.z 2
6498.2.a.ba 2
6498.2.a.bb 2
6498.2.a.bc 2
6498.2.a.bd 2
6498.2.a.be 2
6498.2.a.bf 2
6498.2.a.bg 2
6498.2.a.bh 2
6498.2.a.bi 2
6498.2.a.bj 2
6498.2.a.bk 2
6498.2.a.bl 3
6498.2.a.bm 3
6498.2.a.bn 3
6498.2.a.bo 3
6498.2.a.bp 3
6498.2.a.bq 3
6498.2.a.br 3
6498.2.a.bs 3
6498.2.a.bt 3
6498.2.a.bu 3
6498.2.a.bv 4
6498.2.a.bw 4
6498.2.a.bx 4
6498.2.a.by 4
6498.2.a.bz 4
6498.2.a.ca 4
6498.2.a.cb 6
6498.2.a.cc 6
6498.2.a.cd 6
6498.2.a.ce 6
6498.2.a.cf 8
6498.2.a.cg 8
6498.2.b $$\chi_{6498}(6497, \cdot)$$ n/a 116 1
6498.2.e $$\chi_{6498}(2167, \cdot)$$ n/a 682 2
6498.2.f $$\chi_{6498}(1375, \cdot)$$ n/a 680 2
6498.2.g $$\chi_{6498}(1873, \cdot)$$ n/a 286 2
6498.2.h $$\chi_{6498}(3541, \cdot)$$ n/a 680 2
6498.2.j $$\chi_{6498}(2459, \cdot)$$ n/a 680 2
6498.2.n $$\chi_{6498}(293, \cdot)$$ n/a 680 2
6498.2.p $$\chi_{6498}(2165, \cdot)$$ n/a 680 2
6498.2.s $$\chi_{6498}(791, \cdot)$$ n/a 232 2
6498.2.u $$\chi_{6498}(415, \cdot)$$ n/a 846 6
6498.2.v $$\chi_{6498}(967, \cdot)$$ n/a 2040 6
6498.2.w $$\chi_{6498}(1111, \cdot)$$ n/a 2040 6
6498.2.x $$\chi_{6498}(623, \cdot)$$ n/a 2040 6
6498.2.bb $$\chi_{6498}(2465, \cdot)$$ n/a 672 6
6498.2.bf $$\chi_{6498}(299, \cdot)$$ n/a 2040 6
6498.2.bg $$\chi_{6498}(343, \cdot)$$ n/a 2826 18
6498.2.bj $$\chi_{6498}(341, \cdot)$$ n/a 2232 18
6498.2.bk $$\chi_{6498}(121, \cdot)$$ n/a 13680 36
6498.2.bl $$\chi_{6498}(163, \cdot)$$ n/a 5652 36
6498.2.bm $$\chi_{6498}(7, \cdot)$$ n/a 13680 36
6498.2.bn $$\chi_{6498}(115, \cdot)$$ n/a 13680 36
6498.2.bp $$\chi_{6498}(107, \cdot)$$ n/a 4464 36
6498.2.bs $$\chi_{6498}(113, \cdot)$$ n/a 13680 36
6498.2.bu $$\chi_{6498}(335, \cdot)$$ n/a 13680 36
6498.2.by $$\chi_{6498}(65, \cdot)$$ n/a 13680 36
6498.2.ca $$\chi_{6498}(43, \cdot)$$ n/a 41040 108
6498.2.cb $$\chi_{6498}(25, \cdot)$$ n/a 41040 108
6498.2.cc $$\chi_{6498}(55, \cdot)$$ n/a 17172 108
6498.2.cd $$\chi_{6498}(155, \cdot)$$ n/a 41040 108
6498.2.ch $$\chi_{6498}(53, \cdot)$$ n/a 13824 108
6498.2.cl $$\chi_{6498}(29, \cdot)$$ n/a 41040 108

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6498))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6498)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(722))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1083))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2166))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3249))$$$$^{\oplus 2}$$