# Properties

 Label 972.1 Level 972 Weight 1 Dimension 6 Nonzero newspaces 2 Newform subspaces 4 Sturm bound 52488 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$972 = 2^{2} \cdot 3^{5}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$4$$ Sturm bound: $$52488$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(972))$$.

Total New Old
Modular forms 979 198 781
Cusp forms 34 6 28
Eisenstein series 945 192 753

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6 q + O(q^{10})$$ $$6 q + 3 q^{19} + 3 q^{37} - 6 q^{73} - 12 q^{91} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(972))$$

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
972.1.c $$\chi_{972}(485, \cdot)$$ 972.1.c.a 1 1
972.1.c.b 1
972.1.d $$\chi_{972}(487, \cdot)$$ None 0 1
972.1.f $$\chi_{972}(163, \cdot)$$ None 0 2
972.1.g $$\chi_{972}(161, \cdot)$$ 972.1.g.a 2 2
972.1.g.b 2
972.1.j $$\chi_{972}(55, \cdot)$$ None 0 6
972.1.k $$\chi_{972}(53, \cdot)$$ None 0 6
972.1.n $$\chi_{972}(19, \cdot)$$ None 0 18
972.1.o $$\chi_{972}(17, \cdot)$$ None 0 18
972.1.r $$\chi_{972}(7, \cdot)$$ None 0 54
972.1.s $$\chi_{972}(5, \cdot)$$ None 0 54

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(972))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(972)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(243))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 2}$$