# Properties

 Label 45.3.h Level $45$ Weight $3$ Character orbit 45.h Rep. character $\chi_{45}(14,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $20$ Newform subspaces $1$ Sturm bound $18$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$45 = 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 45.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(45, [\chi])$$.

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

## Trace form

 $$20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + O(q^{10})$$ $$20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31} - 4 q^{34} + 432 q^{36} + 240 q^{39} - 34 q^{40} + 102 q^{41} - 162 q^{45} + 116 q^{46} - 40 q^{49} - 408 q^{50} - 156 q^{51} - 270 q^{54} + 36 q^{55} - 618 q^{56} + 120 q^{59} + 330 q^{60} - 50 q^{61} + 140 q^{64} + 492 q^{65} - 768 q^{66} + 162 q^{69} - 54 q^{70} + 504 q^{74} + 276 q^{75} - 96 q^{76} - 128 q^{79} + 846 q^{81} + 450 q^{84} - 74 q^{85} + 1488 q^{86} - 990 q^{90} - 288 q^{91} + 218 q^{94} - 762 q^{95} - 474 q^{96} - 468 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(45, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.3.h.a $20$ $1.226$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$-12$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots$$