# Properties

 Label 475.2.j Level $475$ Weight $2$ Character orbit 475.j Rep. character $\chi_{475}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $56$ Newform subspaces $4$ Sturm bound $100$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 475.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$100$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(475, [\chi])$$.

Total New Old
Modular forms 112 64 48
Cusp forms 88 56 32
Eisenstein series 24 8 16

## Trace form

 $$56 q + 24 q^{4} + 10 q^{6} + 26 q^{9} + O(q^{10})$$ $$56 q + 24 q^{4} + 10 q^{6} + 26 q^{9} - 20 q^{11} - 16 q^{16} + 16 q^{19} + 10 q^{21} + 26 q^{24} + 68 q^{26} - 6 q^{29} - 44 q^{31} - 22 q^{34} - 14 q^{36} - 56 q^{39} + 10 q^{41} - 30 q^{44} - 96 q^{46} + 16 q^{49} + 26 q^{51} - 12 q^{54} - 88 q^{56} - 20 q^{59} - 42 q^{61} - 72 q^{64} - 64 q^{66} + 4 q^{69} - 12 q^{71} + 24 q^{74} + 140 q^{76} + 2 q^{79} + 36 q^{81} + 108 q^{84} + 30 q^{86} - 12 q^{89} + 46 q^{91} + 8 q^{94} + 100 q^{96} + 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(475, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
475.2.j.a $4$ $3.793$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{4}+2\zeta_{12}^{3}q^{7}+\cdots$$
475.2.j.b $12$ $3.793$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{11}q^{3}+(2-\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots$$
475.2.j.c $16$ $3.793$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{14}q^{2}+(\beta _{7}+\beta _{13})q^{3}+(-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots$$
475.2.j.d $24$ $3.793$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(475, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(475, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 2}$$