# Properties

 Label 45.6.b Level $45$ Weight $6$ Character orbit 45.b Rep. character $\chi_{45}(19,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $4$ Sturm bound $36$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$45 = 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 45.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$36$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(45, [\chi])$$.

Total New Old
Modular forms 34 14 20
Cusp forms 26 12 14
Eisenstein series 8 2 6

## Trace form

 $$12 q - 204 q^{4} - 30 q^{5} + O(q^{10})$$ $$12 q - 204 q^{4} - 30 q^{5} - 360 q^{10} - 840 q^{11} + 2316 q^{14} + 6996 q^{16} - 4032 q^{19} + 180 q^{20} - 2040 q^{25} - 5772 q^{26} + 6756 q^{29} - 11664 q^{31} - 27912 q^{34} - 25320 q^{35} + 69900 q^{40} - 3228 q^{41} + 96084 q^{44} + 22488 q^{46} - 69972 q^{49} - 93000 q^{50} + 88200 q^{55} - 78780 q^{56} + 163992 q^{59} + 83376 q^{61} - 369324 q^{64} - 82680 q^{65} + 72720 q^{70} - 141552 q^{71} + 282276 q^{74} + 298824 q^{76} - 39456 q^{79} - 180060 q^{80} + 12780 q^{85} - 57120 q^{86} + 293508 q^{89} + 147888 q^{91} - 445680 q^{94} - 99960 q^{95} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(45, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.6.b.a $2$ $7.217$ $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{2}-93q^{4}+5\beta q^{5}-61\beta q^{8}+\cdots$$
45.6.b.b $2$ $7.217$ $$\Q(\sqrt{-11})$$ None $$0$$ $$0$$ $$90$$ $$0$$ $$q-\beta q^{2}-12q^{4}+(45-5\beta )q^{5}-9\beta q^{7}+\cdots$$
45.6.b.c $4$ $7.217$ $$\Q(i, \sqrt{89})$$ None $$0$$ $$0$$ $$-120$$ $$0$$ $$q+\beta _{1}q^{2}+(-11+\beta _{3})q^{4}+(-30-5\beta _{1}+\cdots)q^{5}+\cdots$$
45.6.b.d $4$ $7.217$ $$\Q(\sqrt{-5}, \sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+12q^{4}+(5\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(45, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(45, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(5, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 2}$$