# Properties

 Label 6724.2 Level 6724 Weight 2 Dimension 820350 Nonzero newspaces 16 Sturm bound 5648160

## Defining parameters

 Level: $$N$$ = $$6724 = 2^{2} \cdot 41^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$5648160$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6724))$$.

Total New Old
Modular forms 1418140 825070 593070
Cusp forms 1405941 820350 585591
Eisenstein series 12199 4720 7479

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6724))$$

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
6724.2.a $$\chi_{6724}(1, \cdot)$$ 6724.2.a.a 3 1
6724.2.a.b 3
6724.2.a.c 4
6724.2.a.d 4
6724.2.a.e 6
6724.2.a.f 8
6724.2.a.g 8
6724.2.a.h 12
6724.2.a.i 12
6724.2.a.j 16
6724.2.a.k 18
6724.2.a.l 18
6724.2.a.m 24
6724.2.b $$\chi_{6724}(3361, \cdot)$$ n/a 136 1
6724.2.f $$\chi_{6724}(4665, \cdot)$$ n/a 274 2
6724.2.g $$\chi_{6724}(857, \cdot)$$ n/a 544 4
6724.2.i $$\chi_{6724}(847, \cdot)$$ n/a 3124 4
6724.2.k $$\chi_{6724}(761, \cdot)$$ n/a 544 4
6724.2.m $$\chi_{6724}(3569, \cdot)$$ n/a 1096 8
6724.2.o $$\chi_{6724}(719, \cdot)$$ n/a 12496 16
6724.2.q $$\chi_{6724}(165, \cdot)$$ n/a 5760 40
6724.2.t $$\chi_{6724}(81, \cdot)$$ n/a 5760 40
6724.2.u $$\chi_{6724}(9, \cdot)$$ n/a 11440 80
6724.2.w $$\chi_{6724}(37, \cdot)$$ n/a 23040 160
6724.2.x $$\chi_{6724}(3, \cdot)$$ n/a 137440 160
6724.2.ba $$\chi_{6724}(25, \cdot)$$ n/a 23040 160
6724.2.bd $$\chi_{6724}(5, \cdot)$$ n/a 45760 320
6724.2.bf $$\chi_{6724}(7, \cdot)$$ n/a 549760 640

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6724))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6724)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(82))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(164))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1681))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3362))$$$$^{\oplus 2}$$