# Properties

 Label 8016.2 Level 8016 Weight 2 Dimension 751436 Nonzero newspaces 16 Sturm bound 7.13933e+06

## Defining parameters

 Level: $$N$$ = $$8016 = 2^{4} \cdot 3 \cdot 167$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$7139328$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8016))$$.

Total New Old
Modular forms 1794128 754408 1039720
Cusp forms 1775537 751436 1024101
Eisenstein series 18591 2972 15619

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8016))$$

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
8016.2.a $$\chi_{8016}(1, \cdot)$$ 8016.2.a.a 1 1
8016.2.a.b 1
8016.2.a.c 1
8016.2.a.d 1
8016.2.a.e 1
8016.2.a.f 1
8016.2.a.g 1
8016.2.a.h 1
8016.2.a.i 1
8016.2.a.j 1
8016.2.a.k 2
8016.2.a.l 3
8016.2.a.m 3
8016.2.a.n 3
8016.2.a.o 4
8016.2.a.p 5
8016.2.a.q 5
8016.2.a.r 5
8016.2.a.s 5
8016.2.a.t 5
8016.2.a.u 5
8016.2.a.v 7
8016.2.a.w 7
8016.2.a.x 8
8016.2.a.y 8
8016.2.a.z 8
8016.2.a.ba 9
8016.2.a.bb 9
8016.2.a.bc 9
8016.2.a.bd 10
8016.2.a.be 11
8016.2.a.bf 12
8016.2.a.bg 13
8016.2.b $$\chi_{8016}(2671, \cdot)$$ n/a 168 1
8016.2.e $$\chi_{8016}(335, \cdot)$$ n/a 332 1
8016.2.f $$\chi_{8016}(4009, \cdot)$$ None 0 1
8016.2.i $$\chi_{8016}(1001, \cdot)$$ None 0 1
8016.2.j $$\chi_{8016}(4343, \cdot)$$ None 0 1
8016.2.m $$\chi_{8016}(6679, \cdot)$$ None 0 1
8016.2.n $$\chi_{8016}(5009, \cdot)$$ n/a 334 1
8016.2.s $$\chi_{8016}(3005, \cdot)$$ n/a 2680 2
8016.2.t $$\chi_{8016}(2005, \cdot)$$ n/a 1328 2
8016.2.u $$\chi_{8016}(667, \cdot)$$ n/a 1344 2
8016.2.v $$\chi_{8016}(2339, \cdot)$$ n/a 2656 2
8016.2.y $$\chi_{8016}(49, \cdot)$$ n/a 13776 82
8016.2.bb $$\chi_{8016}(17, \cdot)$$ n/a 27388 82
8016.2.bc $$\chi_{8016}(55, \cdot)$$ None 0 82
8016.2.bf $$\chi_{8016}(215, \cdot)$$ None 0 82
8016.2.bg $$\chi_{8016}(41, \cdot)$$ None 0 82
8016.2.bj $$\chi_{8016}(25, \cdot)$$ None 0 82
8016.2.bk $$\chi_{8016}(47, \cdot)$$ n/a 27552 82
8016.2.bn $$\chi_{8016}(79, \cdot)$$ n/a 13776 82
8016.2.bq $$\chi_{8016}(11, \cdot)$$ n/a 219760 164
8016.2.br $$\chi_{8016}(43, \cdot)$$ n/a 110208 164
8016.2.bs $$\chi_{8016}(61, \cdot)$$ n/a 110208 164
8016.2.bt $$\chi_{8016}(5, \cdot)$$ n/a 219760 164

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8016))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8016)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(167))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(334))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(501))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(668))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1002))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1336))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2004))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2672))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4008))$$$$^{\oplus 2}$$