# Properties

 Label 175.2.b Level $175$ Weight $2$ Character orbit 175.b Rep. character $\chi_{175}(99,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $3$ Sturm bound $40$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 175.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$40$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(175, [\chi])$$.

Total New Old
Modular forms 26 10 16
Cusp forms 14 10 4
Eisenstein series 12 0 12

## Trace form

 $$10 q - 4 q^{4} - 8 q^{6} - 14 q^{9} + O(q^{10})$$ $$10 q - 4 q^{4} - 8 q^{6} - 14 q^{9} + 4 q^{11} - 4 q^{14} + 8 q^{16} + 8 q^{19} + 28 q^{24} - 28 q^{29} - 20 q^{31} + 36 q^{34} - 20 q^{36} + 28 q^{39} + 8 q^{41} - 6 q^{44} - 34 q^{46} - 10 q^{49} - 4 q^{51} - 24 q^{54} + 18 q^{56} - 4 q^{59} + 16 q^{61} - 6 q^{64} + 8 q^{66} + 12 q^{69} + 40 q^{71} + 6 q^{74} - 52 q^{76} + 20 q^{79} + 18 q^{81} + 4 q^{84} + 42 q^{86} - 48 q^{89} - 4 q^{91} - 52 q^{94} + 20 q^{96} - 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(175, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.2.b.a $2$ $1.397$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2q^{4}-iq^{7}+2q^{9}-3q^{11}+\cdots$$
175.2.b.b $4$ $1.397$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-3+\beta _{3})q^{4}+\cdots$$
175.2.b.c $4$ $1.397$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2\beta _{1}-2\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(175, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(175, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$