## Defining parameters

 Level: $$N$$ = $$8048 = 2^{4} \cdot 503$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$8096256$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8048))$$.

Total New Old
Modular forms 2031092 1140781 890311
Cusp forms 2017037 1136273 880764
Eisenstein series 14055 4508 9547

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8048))$$

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
8048.2.a $$\chi_{8048}(1, \cdot)$$ 8048.2.a.a 1 1
8048.2.a.b 1
8048.2.a.c 1
8048.2.a.d 1
8048.2.a.e 1
8048.2.a.f 1
8048.2.a.g 1
8048.2.a.h 1
8048.2.a.i 1
8048.2.a.j 1
8048.2.a.k 1
8048.2.a.l 2
8048.2.a.m 3
8048.2.a.n 5
8048.2.a.o 5
8048.2.a.p 10
8048.2.a.q 12
8048.2.a.r 12
8048.2.a.s 21
8048.2.a.t 21
8048.2.a.u 26
8048.2.a.v 28
8048.2.a.w 29
8048.2.a.x 33
8048.2.a.y 33
8048.2.b $$\chi_{8048}(8047, \cdot)$$ n/a 252 1
8048.2.c $$\chi_{8048}(4025, \cdot)$$ None 0 1
8048.2.h $$\chi_{8048}(4023, \cdot)$$ None 0 1
8048.2.j $$\chi_{8048}(2013, \cdot)$$ n/a 2008 2
8048.2.l $$\chi_{8048}(2011, \cdot)$$ n/a 2012 2
8048.2.m $$\chi_{8048}(33, \cdot)$$ n/a 62750 250
8048.2.n $$\chi_{8048}(55, \cdot)$$ None 0 250
8048.2.s $$\chi_{8048}(9, \cdot)$$ None 0 250
8048.2.t $$\chi_{8048}(15, \cdot)$$ n/a 63000 250
8048.2.u $$\chi_{8048}(19, \cdot)$$ n/a 503000 500
8048.2.w $$\chi_{8048}(13, \cdot)$$ n/a 503000 500

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8048))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8048)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(503))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1006))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2012))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4024))$$$$^{\oplus 2}$$