# Properties

 Label 8993.2 Level 8993 Weight 2 Dimension 3305330 Nonzero newspaces 20 Sturm bound 13406976

## Defining parameters

 Level: $$N$$ = $$8993 = 17 \cdot 23^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Sturm bound: $$13406976$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8993))$$.

Total New Old
Modular forms 3363712 3326464 37248
Cusp forms 3339777 3305330 34447
Eisenstein series 23935 21134 2801

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8993))$$

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
8993.2.a $$\chi_{8993}(1, \cdot)$$ 8993.2.a.a 1 1
8993.2.a.b 2
8993.2.a.c 3
8993.2.a.d 3
8993.2.a.e 4
8993.2.a.f 4
8993.2.a.g 9
8993.2.a.h 11
8993.2.a.i 11
8993.2.a.j 12
8993.2.a.k 14
8993.2.a.l 14
8993.2.a.m 15
8993.2.a.n 15
8993.2.a.o 28
8993.2.a.p 28
8993.2.a.q 30
8993.2.a.r 30
8993.2.a.s 60
8993.2.a.t 60
8993.2.a.u 70
8993.2.a.v 70
8993.2.a.w 90
8993.2.a.x 90
8993.2.b $$\chi_{8993}(8465, \cdot)$$ n/a 736 1
8993.2.e $$\chi_{8993}(3175, \cdot)$$ n/a 1472 2
8993.2.g $$\chi_{8993}(2117, \cdot)$$ n/a 2948 4
8993.2.i $$\chi_{8993}(647, \cdot)$$ n/a 6720 10
8993.2.k $$\chi_{8993}(1057, \cdot)$$ n/a 5888 8
8993.2.n $$\chi_{8993}(118, \cdot)$$ n/a 7360 10
8993.2.o $$\chi_{8993}(392, \cdot)$$ n/a 16192 22
8993.2.q $$\chi_{8993}(795, \cdot)$$ n/a 14720 20
8993.2.t $$\chi_{8993}(254, \cdot)$$ n/a 18172 22
8993.2.v $$\chi_{8993}(399, \cdot)$$ n/a 29440 40
8993.2.x $$\chi_{8993}(47, \cdot)$$ n/a 36344 44
8993.2.y $$\chi_{8993}(28, \cdot)$$ n/a 58880 80
8993.2.bb $$\chi_{8993}(70, \cdot)$$ n/a 72688 88
8993.2.bc $$\chi_{8993}(18, \cdot)$$ n/a 161920 220
8993.2.bd $$\chi_{8993}(22, \cdot)$$ n/a 145376 176
8993.2.bf $$\chi_{8993}(16, \cdot)$$ n/a 181720 220
8993.2.bi $$\chi_{8993}(4, \cdot)$$ n/a 363440 440
8993.2.bk $$\chi_{8993}(2, \cdot)$$ n/a 726880 880
8993.2.bn $$\chi_{8993}(5, \cdot)$$ n/a 1453760 1760

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8993))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8993)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(391))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(529))$$$$^{\oplus 2}$$