Properties

 Label 2004.1 Level 2004 Weight 1 Dimension 26 Nonzero newspaces 1 Newforms 6 Sturm bound 223104 Trace bound 0

Defining parameters

 Level: $$N$$ = $$2004 = 2^{2} \cdot 3 \cdot 167$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newforms: $$6$$ Sturm bound: $$223104$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2004))$$.

Total New Old
Modular forms 1716 358 1358
Cusp forms 56 26 30
Eisenstein series 1660 332 1328

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 26 0 0 0

Trace form

 $$26q$$ $$\mathstrut +\mathstrut 4q^{4}$$ $$\mathstrut -\mathstrut 4q^{6}$$ $$\mathstrut +\mathstrut 4q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$26q$$ $$\mathstrut +\mathstrut 4q^{4}$$ $$\mathstrut -\mathstrut 4q^{6}$$ $$\mathstrut +\mathstrut 4q^{9}$$ $$\mathstrut +\mathstrut 4q^{16}$$ $$\mathstrut -\mathstrut 4q^{24}$$ $$\mathstrut -\mathstrut 18q^{25}$$ $$\mathstrut +\mathstrut 4q^{36}$$ $$\mathstrut -\mathstrut 11q^{42}$$ $$\mathstrut -\mathstrut 11q^{48}$$ $$\mathstrut -\mathstrut 18q^{49}$$ $$\mathstrut +\mathstrut 7q^{54}$$ $$\mathstrut +\mathstrut 4q^{64}$$ $$\mathstrut +\mathstrut 11q^{72}$$ $$\mathstrut +\mathstrut 4q^{81}$$ $$\mathstrut +\mathstrut 11q^{84}$$ $$\mathstrut -\mathstrut 8q^{85}$$ $$\mathstrut -\mathstrut 4q^{96}$$ $$\mathstrut -\mathstrut 8q^{97}$$ $$\mathstrut +\mathstrut O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2004))$$

We only show spaces with odd 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
2004.1.d $$\chi_{2004}(1337, \cdot)$$ None 0 1
2004.1.e $$\chi_{2004}(1669, \cdot)$$ None 0 1
2004.1.f $$\chi_{2004}(1003, \cdot)$$ None 0 1
2004.1.g $$\chi_{2004}(2003, \cdot)$$ 2004.1.g.a 1 1
2004.1.g.b 1
2004.1.g.c 2
2004.1.g.d 2
2004.1.g.e 10
2004.1.g.f 10
2004.1.k $$\chi_{2004}(23, \cdot)$$ None 0 82
2004.1.l $$\chi_{2004}(7, \cdot)$$ None 0 82
2004.1.m $$\chi_{2004}(13, \cdot)$$ None 0 82
2004.1.n $$\chi_{2004}(29, \cdot)$$ None 0 82

Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(2004))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(2004)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(167))$$$$^{\oplus 6}$$