# Properties

 Label 252.1 Level 252 Weight 1 Dimension 6 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 3456 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$3456$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(252))$$.

Total New Old
Modular forms 253 50 203
Cusp forms 13 6 7
Eisenstein series 240 44 196

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

 $$6 q + q^{7} + O(q^{10})$$ $$6 q + q^{7} - 4 q^{16} - 3 q^{19} - 4 q^{22} - 5 q^{25} + 4 q^{28} - 3 q^{31} - q^{37} + 2 q^{43} + 4 q^{46} - 5 q^{49} + 4 q^{58} + q^{67} + 3 q^{73} + q^{79} + 4 q^{88} + 3 q^{91} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(252))$$

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
252.1.c $$\chi_{252}(197, \cdot)$$ None 0 1
252.1.d $$\chi_{252}(181, \cdot)$$ None 0 1
252.1.g $$\chi_{252}(127, \cdot)$$ None 0 1
252.1.h $$\chi_{252}(251, \cdot)$$ 252.1.h.a 4 1
252.1.m $$\chi_{252}(65, \cdot)$$ None 0 2
252.1.p $$\chi_{252}(61, \cdot)$$ None 0 2
252.1.q $$\chi_{252}(143, \cdot)$$ None 0 2
252.1.r $$\chi_{252}(131, \cdot)$$ None 0 2
252.1.s $$\chi_{252}(83, \cdot)$$ None 0 2
252.1.u $$\chi_{252}(151, \cdot)$$ None 0 2
252.1.v $$\chi_{252}(43, \cdot)$$ None 0 2
252.1.y $$\chi_{252}(163, \cdot)$$ None 0 2
252.1.z $$\chi_{252}(73, \cdot)$$ 252.1.z.a 2 2
252.1.bc $$\chi_{252}(13, \cdot)$$ None 0 2
252.1.bd $$\chi_{252}(229, \cdot)$$ None 0 2
252.1.bg $$\chi_{252}(29, \cdot)$$ None 0 2
252.1.bh $$\chi_{252}(137, \cdot)$$ None 0 2
252.1.bk $$\chi_{252}(53, \cdot)$$ None 0 2
252.1.bl $$\chi_{252}(67, \cdot)$$ None 0 2
252.1.bn $$\chi_{252}(47, \cdot)$$ None 0 2

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(252))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(252)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 2}$$