## Defining parameters

 Level: $$N$$ = $$2004 = 2^{2} \cdot 3 \cdot 167$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$446208$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2004))$$.

Total New Old
Modular forms 113212 49128 64084
Cusp forms 109893 48472 61421
Eisenstein series 3319 656 2663

## Trace form

 $$48472q - 166q^{4} - 83q^{6} - 166q^{9} + O(q^{10})$$ $$48472q - 166q^{4} - 83q^{6} - 166q^{9} - 166q^{10} - 83q^{12} - 332q^{13} - 166q^{16} - 83q^{18} - 166q^{21} - 166q^{22} - 83q^{24} - 332q^{25} - 166q^{28} - 83q^{30} - 166q^{33} - 166q^{34} - 83q^{36} - 332q^{37} - 166q^{40} - 83q^{42} - 166q^{45} - 166q^{46} - 83q^{48} - 332q^{49} - 166q^{52} - 83q^{54} - 166q^{57} - 166q^{58} - 83q^{60} - 332q^{61} - 166q^{64} - 83q^{66} - 166q^{69} - 166q^{70} - 83q^{72} - 332q^{73} - 166q^{76} - 83q^{78} - 166q^{81} - 166q^{82} - 83q^{84} - 332q^{85} - 166q^{88} - 83q^{90} - 166q^{93} - 166q^{94} - 83q^{96} - 332q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2004))$$

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
2004.2.a $$\chi_{2004}(1, \cdot)$$ 2004.2.a.a 5 1
2004.2.a.b 5
2004.2.a.c 9
2004.2.a.d 9
2004.2.b $$\chi_{2004}(667, \cdot)$$ n/a 168 1
2004.2.c $$\chi_{2004}(335, \cdot)$$ n/a 332 1
2004.2.h $$\chi_{2004}(1001, \cdot)$$ 2004.2.h.a 56 1
2004.2.i $$\chi_{2004}(25, \cdot)$$ n/a 2296 82
2004.2.j $$\chi_{2004}(5, \cdot)$$ n/a 4592 82
2004.2.o $$\chi_{2004}(11, \cdot)$$ n/a 27224 82
2004.2.p $$\chi_{2004}(43, \cdot)$$ n/a 13776 82

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2004))$$ into lower level spaces

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