# Properties

 Label 84.1 Level 84 Weight 1 Dimension 2 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 384 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$84 = 2^{2} \cdot 3 \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$384$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(84))$$.

Total New Old
Modular forms 62 14 48
Cusp forms 2 2 0
Eisenstein series 60 12 48

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q - q^{3} - q^{7} - q^{9} + O(q^{10})$$ $$2 q - q^{3} - q^{7} - q^{9} - 2 q^{13} + q^{19} + 2 q^{21} - q^{25} + 2 q^{27} + q^{31} + q^{37} + q^{39} - 2 q^{43} - q^{49} - 2 q^{57} - 2 q^{61} - q^{63} + q^{67} + q^{73} - q^{75} + q^{79} - q^{81} + q^{91} + q^{93} + 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(84))$$

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
84.1.c $$\chi_{84}(29, \cdot)$$ None 0 1
84.1.d $$\chi_{84}(13, \cdot)$$ None 0 1
84.1.g $$\chi_{84}(43, \cdot)$$ None 0 1
84.1.h $$\chi_{84}(83, \cdot)$$ None 0 1
84.1.j $$\chi_{84}(47, \cdot)$$ None 0 2
84.1.l $$\chi_{84}(67, \cdot)$$ None 0 2
84.1.m $$\chi_{84}(61, \cdot)$$ None 0 2
84.1.p $$\chi_{84}(53, \cdot)$$ 84.1.p.a 2 2