# Properties

 Label 175.2.k Level $175$ Weight $2$ Character orbit 175.k Rep. character $\chi_{175}(74,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $20$ Newform subspaces $2$ Sturm bound $40$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 175.k (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$40$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 52 28 24
Cusp forms 28 20 8
Eisenstein series 24 8 16

## Trace form

 $$20q + 10q^{4} - 16q^{6} + 8q^{9} + O(q^{10})$$ $$20q + 10q^{4} - 16q^{6} + 8q^{9} - 4q^{11} - 26q^{14} - 2q^{16} - 8q^{19} + 6q^{21} - 16q^{24} - 6q^{26} + 40q^{29} + 14q^{31} - 4q^{36} + 32q^{39} - 44q^{41} - 12q^{44} + 16q^{46} - 44q^{49} - 14q^{51} - 42q^{54} - 6q^{56} - 26q^{59} + 2q^{61} + 120q^{64} - 44q^{66} - 24q^{69} - 4q^{71} - 30q^{74} + 124q^{76} + 34q^{79} + 30q^{81} + 2q^{84} + 48q^{86} - 24q^{89} - 62q^{91} - 26q^{94} - 14q^{96} - 20q^{99} + O(q^{100})$$

## 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.k.a $$8$$ $$1.397$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{3}q^{2}-\zeta_{24}^{4}q^{3}+(1-\zeta_{24}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots$$
175.2.k.b $$12$$ $$1.397$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{10}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots$$

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

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