# Properties

 Label 476.1 Level 476 Weight 1 Dimension 8 Nonzero newspaces 1 Newform subspaces 3 Sturm bound 13824 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$476 = 2^{2} \cdot 7 \cdot 17$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$3$$ Sturm bound: $$13824$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(476))$$.

Total New Old
Modular forms 506 160 346
Cusp forms 26 8 18
Eisenstein series 480 152 328

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 0 0

## Trace form

 $$8 q - 4 q^{4} - 4 q^{9} + O(q^{10})$$ $$8 q - 4 q^{4} - 4 q^{9} - 4 q^{16} - 4 q^{17} + 4 q^{18} - 4 q^{21} - 4 q^{25} + 4 q^{26} + 4 q^{33} + 8 q^{36} - 4 q^{42} + 4 q^{53} + 8 q^{64} - 8 q^{66} - 4 q^{68} - 8 q^{69} + 4 q^{72} + 8 q^{77} + 8 q^{84} + 4 q^{93} - 4 q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(476))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
476.1.c $$\chi_{476}(69, \cdot)$$ None 0 1
476.1.d $$\chi_{476}(239, \cdot)$$ None 0 1
476.1.g $$\chi_{476}(407, \cdot)$$ None 0 1
476.1.h $$\chi_{476}(237, \cdot)$$ None 0 1
476.1.j $$\chi_{476}(13, \cdot)$$ None 0 2
476.1.m $$\chi_{476}(183, \cdot)$$ None 0 2
476.1.n $$\chi_{476}(33, \cdot)$$ None 0 2
476.1.o $$\chi_{476}(67, \cdot)$$ 476.1.o.a 2 2
476.1.o.b 2
476.1.o.c 4
476.1.r $$\chi_{476}(375, \cdot)$$ None 0 2
476.1.s $$\chi_{476}(341, \cdot)$$ None 0 2
476.1.v $$\chi_{476}(15, \cdot)$$ None 0 4
476.1.x $$\chi_{476}(321, \cdot)$$ None 0 4
476.1.y $$\chi_{476}(89, \cdot)$$ None 0 4
476.1.bb $$\chi_{476}(123, \cdot)$$ None 0 4
476.1.bc $$\chi_{476}(29, \cdot)$$ None 0 8
476.1.bf $$\chi_{476}(27, \cdot)$$ None 0 8
476.1.bg $$\chi_{476}(151, \cdot)$$ None 0 8
476.1.bi $$\chi_{476}(117, \cdot)$$ None 0 8
476.1.bk $$\chi_{476}(3, \cdot)$$ None 0 16
476.1.bn $$\chi_{476}(37, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(476))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(476)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(476))$$$$^{\oplus 1}$$