# Properties

 Label 483.3.f Level $483$ Weight $3$ Character orbit 483.f Rep. character $\chi_{483}(22,\cdot)$ Character field $\Q$ Dimension $48$ Newform subspaces $1$ Sturm bound $192$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$483 = 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 483.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$23$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$192$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(483, [\chi])$$.

Total New Old
Modular forms 132 48 84
Cusp forms 124 48 76
Eisenstein series 8 0 8

## Trace form

 $$48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10})$$ $$48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(483, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
483.3.f.a $$48$$ $$13.161$$ None $$4$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(483, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(483, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(23, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(69, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(161, [\chi])$$$$^{\oplus 2}$$