# Properties

 Label 2001.1 Level 2001 Weight 1 Dimension 84 Nonzero newspaces 2 Newforms 8 Sturm bound 295680 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$2001 = 3 \cdot 23 \cdot 29$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newforms: $$8$$ Sturm bound: $$295680$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2001))$$.

Total New Old
Modular forms 2634 1220 1414
Cusp forms 170 84 86
Eisenstein series 2464 1136 1328

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 84 0 0 0

## Trace form

 $$84q$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$84q$$ $$\mathstrut -\mathstrut 84q^{64}$$ $$\mathstrut +\mathstrut 42q^{72}$$ $$\mathstrut -\mathstrut 42q^{96}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2001))$$

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
2001.1.b $$\chi_{2001}(1333, \cdot)$$ None 0 1
2001.1.c $$\chi_{2001}(668, \cdot)$$ None 0 1
2001.1.f $$\chi_{2001}(436, \cdot)$$ None 0 1
2001.1.g $$\chi_{2001}(1565, \cdot)$$ None 0 1
2001.1.i $$\chi_{2001}(1172, \cdot)$$ 2001.1.i.a 2 2
2001.1.i.b 2
2001.1.i.c 4
2001.1.i.d 4
2001.1.j $$\chi_{2001}(70, \cdot)$$ None 0 2
2001.1.p $$\chi_{2001}(254, \cdot)$$ None 0 6
2001.1.q $$\chi_{2001}(574, \cdot)$$ None 0 6
2001.1.t $$\chi_{2001}(806, \cdot)$$ None 0 6
2001.1.u $$\chi_{2001}(22, \cdot)$$ None 0 6
2001.1.w $$\chi_{2001}(173, \cdot)$$ None 0 10
2001.1.x $$\chi_{2001}(88, \cdot)$$ None 0 10
2001.1.ba $$\chi_{2001}(59, \cdot)$$ None 0 10
2001.1.bb $$\chi_{2001}(28, \cdot)$$ None 0 10
2001.1.be $$\chi_{2001}(346, \cdot)$$ None 0 12
2001.1.bf $$\chi_{2001}(68, \cdot)$$ 2001.1.bf.a 12 12
2001.1.bf.b 12
2001.1.bf.c 24
2001.1.bf.d 24
2001.1.bi $$\chi_{2001}(133, \cdot)$$ None 0 20
2001.1.bj $$\chi_{2001}(17, \cdot)$$ None 0 20
2001.1.bl $$\chi_{2001}(34, \cdot)$$ None 0 60
2001.1.bm $$\chi_{2001}(110, \cdot)$$ None 0 60
2001.1.bp $$\chi_{2001}(7, \cdot)$$ None 0 60
2001.1.bq $$\chi_{2001}(35, \cdot)$$ None 0 60
2001.1.bs $$\chi_{2001}(11, \cdot)$$ None 0 120
2001.1.bt $$\chi_{2001}(31, \cdot)$$ None 0 120

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(2001))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(2001)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(667))$$$$^{\oplus 2}$$