# Properties

 Label 175.3.j Level $175$ Weight $3$ Character orbit 175.j Rep. character $\chi_{175}(24,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $44$ Newform subspaces $2$ Sturm bound $60$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 175.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$60$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(175, [\chi])$$.

Total New Old
Modular forms 92 52 40
Cusp forms 68 44 24
Eisenstein series 24 8 16

## Trace form

 $$44 q + 42 q^{4} - 32 q^{9} + O(q^{10})$$ $$44 q + 42 q^{4} - 32 q^{9} - 8 q^{11} + 74 q^{14} - 50 q^{16} - 72 q^{19} - 18 q^{21} - 180 q^{24} - 78 q^{26} + 32 q^{29} + 78 q^{31} + 348 q^{36} + 204 q^{39} + 60 q^{44} - 160 q^{46} + 364 q^{49} - 210 q^{51} - 366 q^{54} - 190 q^{56} - 558 q^{59} - 282 q^{61} - 8 q^{64} + 420 q^{66} - 308 q^{71} + 538 q^{74} + 122 q^{79} - 166 q^{81} + 1506 q^{84} + 200 q^{86} - 924 q^{89} - 474 q^{91} - 1506 q^{94} + 1170 q^{96} - 508 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(175, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.3.j.a $20$ $4.768$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{13}q^{2}+(-\beta _{12}+\beta _{15})q^{3}+(-2\beta _{4}+\cdots)q^{4}+\cdots$$
175.3.j.b $24$ $4.768$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(175, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(175, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$