# Properties

 Label 4008.2 Level 4008 Weight 2 Dimension 187570 Nonzero newspaces 12 Sturm bound 1.78483e+06

## Defining parameters

 Level: $$N$$ = $$4008 = 2^{3} \cdot 3 \cdot 167$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Sturm bound: $$1784832$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4008))$$.

Total New Old
Modular forms 450192 188890 261302
Cusp forms 442225 187570 254655
Eisenstein series 7967 1320 6647

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4008))$$

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
4008.2.a $$\chi_{4008}(1, \cdot)$$ 4008.2.a.a 1 1
4008.2.a.b 1
4008.2.a.c 1
4008.2.a.d 1
4008.2.a.e 3
4008.2.a.f 5
4008.2.a.g 7
4008.2.a.h 8
4008.2.a.i 9
4008.2.a.j 10
4008.2.a.k 11
4008.2.a.l 12
4008.2.a.m 13
4008.2.b $$\chi_{4008}(2671, \cdot)$$ None 0 1
4008.2.e $$\chi_{4008}(335, \cdot)$$ None 0 1
4008.2.f $$\chi_{4008}(2005, \cdot)$$ n/a 332 1
4008.2.i $$\chi_{4008}(3005, \cdot)$$ n/a 668 1
4008.2.j $$\chi_{4008}(2339, \cdot)$$ n/a 664 1
4008.2.m $$\chi_{4008}(667, \cdot)$$ n/a 336 1
4008.2.n $$\chi_{4008}(1001, \cdot)$$ n/a 168 1
4008.2.q $$\chi_{4008}(25, \cdot)$$ n/a 6888 82
4008.2.t $$\chi_{4008}(17, \cdot)$$ n/a 13776 82
4008.2.u $$\chi_{4008}(43, \cdot)$$ n/a 27552 82
4008.2.x $$\chi_{4008}(11, \cdot)$$ n/a 54776 82
4008.2.y $$\chi_{4008}(5, \cdot)$$ n/a 54776 82
4008.2.bb $$\chi_{4008}(61, \cdot)$$ n/a 27552 82
4008.2.bc $$\chi_{4008}(47, \cdot)$$ None 0 82
4008.2.bf $$\chi_{4008}(55, \cdot)$$ None 0 82

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4008))$$ into lower level spaces

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