# Properties

 Label 1444.1 Level 1444 Weight 1 Dimension 62 Nonzero newspaces 6 Newform subspaces 11 Sturm bound 129960 Trace bound 1

# Learn more about

## Defining parameters

 Level: $$N$$ = $$1444 = 2^{2} \cdot 19^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$6$$ Newform subspaces: $$11$$ Sturm bound: $$129960$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1444))$$.

Total New Old
Modular forms 1324 531 793
Cusp forms 64 62 2
Eisenstein series 1260 469 791

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 44 0 18 0

## Trace form

 $$62q + q^{5} + q^{7} - q^{9} + O(q^{10})$$ $$62q + q^{5} + q^{7} - q^{9} + q^{11} + q^{17} - 18q^{20} - 2q^{23} - q^{35} + q^{43} + q^{45} + q^{47} - q^{55} - 18q^{58} + q^{61} + q^{63} + q^{73} - 10q^{77} - q^{81} - 2q^{83} - q^{85} + q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1444))$$

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
1444.1.b $$\chi_{1444}(723, \cdot)$$ 1444.1.b.a 2 1
1444.1.b.b 2
1444.1.c $$\chi_{1444}(721, \cdot)$$ 1444.1.c.a 2 1
1444.1.g $$\chi_{1444}(1151, \cdot)$$ 1444.1.g.a 4 2
1444.1.g.b 4
1444.1.h $$\chi_{1444}(69, \cdot)$$ 1444.1.h.a 2 2
1444.1.h.b 4
1444.1.j $$\chi_{1444}(333, \cdot)$$ 1444.1.j.a 6 6
1444.1.j.b 12
1444.1.l $$\chi_{1444}(99, \cdot)$$ 1444.1.l.a 12 6
1444.1.l.b 12
1444.1.o $$\chi_{1444}(37, \cdot)$$ None 0 18
1444.1.p $$\chi_{1444}(39, \cdot)$$ None 0 18
1444.1.r $$\chi_{1444}(65, \cdot)$$ None 0 36
1444.1.s $$\chi_{1444}(7, \cdot)$$ None 0 36
1444.1.v $$\chi_{1444}(23, \cdot)$$ None 0 108
1444.1.x $$\chi_{1444}(13, \cdot)$$ None 0 108

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1444))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1444)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 2}$$