# Properties

 Label 45.4.b Level $45$ Weight $4$ Character orbit 45.b Rep. character $\chi_{45}(19,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $24$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$45 = 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 45.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(45, [\chi])$$.

Total New Old
Modular forms 22 8 14
Cusp forms 14 6 8
Eisenstein series 8 2 6

## Trace form

 $$6 q - 12 q^{4} - 6 q^{5} + O(q^{10})$$ $$6 q - 12 q^{4} - 6 q^{5} - 36 q^{10} + 84 q^{11} - 228 q^{14} - 12 q^{16} + 216 q^{19} + 396 q^{20} + 6 q^{25} + 12 q^{26} - 636 q^{29} - 360 q^{31} - 96 q^{34} + 300 q^{35} - 132 q^{40} + 816 q^{41} - 1116 q^{44} + 624 q^{46} + 546 q^{49} + 696 q^{50} - 864 q^{55} - 60 q^{56} - 372 q^{59} - 36 q^{61} - 108 q^{64} - 948 q^{65} + 1080 q^{70} + 72 q^{71} + 3132 q^{74} - 1464 q^{76} - 1368 q^{79} - 444 q^{80} + 2592 q^{85} - 4296 q^{86} + 2232 q^{89} + 1944 q^{91} + 792 q^{94} - 2784 q^{95} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(45, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.4.b.a $2$ $2.655$ $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{2}+3q^{4}+5\beta q^{5}+11\beta q^{8}-5^{2}q^{10}+\cdots$$
45.4.b.b $4$ $2.655$ $$\Q(i, \sqrt{41})$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q-\beta _{1}q^{2}+(-5+\beta _{3})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(45, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(45, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 2}$$