# Properties

 Label 483.2.q Level $483$ Weight $2$ Character orbit 483.q Rep. character $\chi_{483}(64,\cdot)$ Character field $\Q(\zeta_{11})$ Dimension $240$ Newform subspaces $6$ Sturm bound $128$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$483 = 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 483.q (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$23$$ Character field: $$\Q(\zeta_{11})$$ Newform subspaces: $$6$$ Sturm bound: $$128$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 680 240 440
Cusp forms 600 240 360
Eisenstein series 80 0 80

## Trace form

 $$240q + 4q^{2} - 12q^{4} + 8q^{6} + 4q^{7} + 12q^{8} - 24q^{9} + O(q^{10})$$ $$240q + 4q^{2} - 12q^{4} + 8q^{6} + 4q^{7} + 12q^{8} - 24q^{9} + 8q^{10} + 16q^{11} + 16q^{13} + 4q^{14} + 16q^{15} - 32q^{16} - 28q^{17} + 4q^{18} - 12q^{19} + 40q^{20} + 4q^{21} - 24q^{22} - 20q^{23} + 24q^{24} - 44q^{25} - 32q^{26} + 12q^{28} - 12q^{29} + 16q^{30} + 12q^{31} + 24q^{32} + 8q^{33} - 12q^{34} + 8q^{35} - 34q^{36} - 4q^{37} + 32q^{38} - 72q^{39} + 20q^{40} - 64q^{41} + 4q^{42} + 4q^{43} - 74q^{44} - 112q^{46} - 104q^{47} - 144q^{48} - 24q^{49} - 70q^{50} - 4q^{51} + 96q^{52} - 40q^{53} - 36q^{54} - 60q^{55} + 36q^{56} - 28q^{57} + 58q^{58} + 56q^{59} + 12q^{60} + 64q^{61} + 120q^{62} + 4q^{63} - 44q^{64} + 24q^{65} + 64q^{66} + 36q^{67} + 112q^{68} + 24q^{69} + 8q^{70} + 88q^{71} + 12q^{72} + 20q^{73} + 122q^{74} + 16q^{75} - 148q^{76} - 72q^{77} + 8q^{78} - 16q^{79} + 224q^{80} - 24q^{81} - 104q^{82} - 56q^{83} + 12q^{84} + 44q^{85} - 232q^{86} + 40q^{87} + 162q^{88} - 192q^{89} + 8q^{90} - 152q^{91} + 168q^{92} + 56q^{93} + 136q^{94} - 16q^{95} + 8q^{96} - 176q^{97} - 18q^{98} + 16q^{99} + O(q^{100})$$

## 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.q.a $$10$$ $$3.857$$ $$\Q(\zeta_{22})$$ None $$4$$ $$-1$$ $$1$$ $$-1$$ $$q+(-\zeta_{22}^{2}+\zeta_{22}^{3}+\zeta_{22}^{5}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots$$
483.2.q.b $$10$$ $$3.857$$ $$\Q(\zeta_{22})$$ None $$5$$ $$-1$$ $$-5$$ $$-1$$ $$q+(\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots$$
483.2.q.c $$20$$ $$3.857$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-4$$ $$-2$$ $$-1$$ $$-2$$ $$q+(-\beta _{2}-\beta _{6})q^{2}+\beta _{12}q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots$$
483.2.q.d $$60$$ $$3.857$$ None $$-1$$ $$6$$ $$-13$$ $$-6$$
483.2.q.e $$60$$ $$3.857$$ None $$-1$$ $$6$$ $$5$$ $$6$$
483.2.q.f $$80$$ $$3.857$$ None $$1$$ $$-8$$ $$13$$ $$8$$

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

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