# Properties

 Label 475.2.b Level $475$ Weight $2$ Character orbit 475.b Rep. character $\chi_{475}(324,\cdot)$ Character field $\Q$ Dimension $28$ Newform subspaces $5$ Sturm bound $100$ Trace bound $6$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 56 28 28
Cusp forms 44 28 16
Eisenstein series 12 0 12

## Trace form

 $$28 q - 30 q^{4} - 4 q^{6} - 20 q^{9} + O(q^{10})$$ $$28 q - 30 q^{4} - 4 q^{6} - 20 q^{9} + 2 q^{11} + 24 q^{14} + 34 q^{16} - 4 q^{19} - 40 q^{21} + 28 q^{24} - 8 q^{26} + 24 q^{29} - 4 q^{31} - 20 q^{34} + 26 q^{36} + 20 q^{39} + 20 q^{41} + 24 q^{44} + 12 q^{46} - 22 q^{49} - 32 q^{51} + 36 q^{54} - 80 q^{56} + 44 q^{59} + 6 q^{61} - 54 q^{64} + 4 q^{66} - 40 q^{69} - 60 q^{71} - 48 q^{74} + 10 q^{76} + 16 q^{79} - 36 q^{81} + 60 q^{84} + 36 q^{86} - 4 q^{91} - 8 q^{94} - 16 q^{96} + 2 q^{99} + O(q^{100})$$

## 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.b.a $2$ $3.793$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+2q^{4}-iq^{7}-q^{9}+3q^{11}+\cdots$$
475.2.b.b $6$ $3.793$ 6.0.1827904.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}+\beta _{5})q^{2}+(\beta _{1}+\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots$$
475.2.b.c $6$ $3.793$ 6.0.153664.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots$$
475.2.b.d $6$ $3.793$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(\beta _{2}-\beta _{4})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{6}+\cdots$$
475.2.b.e $8$ $3.793$ 8.0.2058981376.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+\beta _{1}q^{3}+(-2-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$$

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

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