# Properties

 Label 135.3.h Level $135$ Weight $3$ Character orbit 135.h Rep. character $\chi_{135}(44,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $20$ Newform subspaces $1$ Sturm bound $54$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$135 = 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 135.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$54$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(135, [\chi])$$.

Total New Old
Modular forms 84 28 56
Cusp forms 60 20 40
Eisenstein series 24 8 16

## Trace form

 $$20 q - 18 q^{4} + 12 q^{5} + O(q^{10})$$ $$20 q - 18 q^{4} + 12 q^{5} + 4 q^{10} + 24 q^{11} - 30 q^{14} - 26 q^{16} - 8 q^{19} - 144 q^{20} + 2 q^{25} + 114 q^{29} + 28 q^{31} - 4 q^{34} - 34 q^{40} - 102 q^{41} + 116 q^{46} - 40 q^{49} + 408 q^{50} + 36 q^{55} + 618 q^{56} - 120 q^{59} - 50 q^{61} + 140 q^{64} - 492 q^{65} - 54 q^{70} - 504 q^{74} - 96 q^{76} - 128 q^{79} - 74 q^{85} - 1488 q^{86} - 288 q^{91} + 218 q^{94} + 762 q^{95} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(135, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.3.h.a $20$ $3.678$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$12$$ $$0$$ $$q+\beta _{2}q^{2}+(-2+\beta _{3}-2\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(135, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(135, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$