# Properties

 Label 483.2.i Level $483$ Weight $2$ Character orbit 483.i Rep. character $\chi_{483}(277,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $60$ Newform subspaces $8$ Sturm bound $128$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$483 = 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 483.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$8$$ Sturm bound: $$128$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$2$$, $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(483, [\chi])$$.

Total New Old
Modular forms 136 60 76
Cusp forms 120 60 60
Eisenstein series 16 0 16

## Trace form

 $$60 q + 2 q^{3} - 32 q^{4} - 8 q^{6} + 6 q^{7} + 24 q^{8} - 30 q^{9} + O(q^{10})$$ $$60 q + 2 q^{3} - 32 q^{4} - 8 q^{6} + 6 q^{7} + 24 q^{8} - 30 q^{9} - 16 q^{10} + 4 q^{12} - 4 q^{13} - 12 q^{14} + 8 q^{15} - 52 q^{16} - 8 q^{17} - 6 q^{19} - 16 q^{20} - 8 q^{21} + 48 q^{22} - 46 q^{25} + 32 q^{26} - 4 q^{27} + 28 q^{28} + 24 q^{29} + 22 q^{31} - 24 q^{32} - 12 q^{33} - 16 q^{34} + 4 q^{35} + 64 q^{36} - 10 q^{37} - 20 q^{38} + 2 q^{39} - 36 q^{40} + 8 q^{41} + 16 q^{42} - 12 q^{43} - 16 q^{44} - 8 q^{47} - 16 q^{48} + 50 q^{49} - 40 q^{50} + 4 q^{54} - 48 q^{55} - 8 q^{56} + 12 q^{57} + 24 q^{58} - 20 q^{59} + 12 q^{60} - 16 q^{61} + 24 q^{62} - 6 q^{63} + 200 q^{64} + 36 q^{65} - 24 q^{66} - 10 q^{67} - 12 q^{68} - 16 q^{69} + 16 q^{70} + 8 q^{71} - 12 q^{72} + 18 q^{73} - 12 q^{74} + 14 q^{75} + 24 q^{76} + 8 q^{77} - 8 q^{78} - 10 q^{79} + 92 q^{80} - 30 q^{81} + 24 q^{82} + 56 q^{83} + 4 q^{84} - 72 q^{85} - 44 q^{86} + 20 q^{87} - 80 q^{88} + 32 q^{90} - 46 q^{91} - 6 q^{93} - 20 q^{94} - 24 q^{95} + 4 q^{96} + 40 q^{97} - 40 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(483, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
483.2.i.a $2$ $3.857$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$1$$ $$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots$$
483.2.i.b $2$ $3.857$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$5$$ $$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots$$
483.2.i.c $2$ $3.857$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-1$$ $$-5$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
483.2.i.d $2$ $3.857$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$3$$ $$-1$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
483.2.i.e $4$ $3.857$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$1$$ $$-2$$ $$1$$ $$10$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$$
483.2.i.f $12$ $3.857$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$1$$ $$6$$ $$-3$$ $$-2$$ $$q+(-\beta _{1}-\beta _{5})q^{2}+\beta _{7}q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots$$
483.2.i.g $16$ $3.857$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-1$$ $$-8$$ $$-5$$ $$-2$$ $$q+(\beta _{1}-\beta _{5})q^{2}+(-1-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots$$
483.2.i.h $20$ $3.857$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-3$$ $$10$$ $$5$$ $$0$$ $$q+(\beta _{1}+\beta _{4})q^{2}-\beta _{9}q^{3}+(-\beta _{1}-\beta _{8}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(483, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(483, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(161, [\chi])$$$$^{\oplus 2}$$