# Properties

 Label 507.2.t Level $507$ Weight $2$ Character orbit 507.t Rep. character $\chi_{507}(4,\cdot)$ Character field $\Q(\zeta_{78})$ Dimension $696$ Newform subspaces $2$ Sturm bound $121$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$507 = 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 507.t (of order $$78$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$169$$ Character field: $$\Q(\zeta_{78})$$ Newform subspaces: $$2$$ Sturm bound: $$121$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(507, [\chi])$$.

Total New Old
Modular forms 1512 696 816
Cusp forms 1416 696 720
Eisenstein series 96 0 96

## Trace form

 $$696q - q^{3} - 26q^{4} + 3q^{7} + 29q^{9} + O(q^{10})$$ $$696q - q^{3} - 26q^{4} + 3q^{7} + 29q^{9} + 4q^{10} + 6q^{11} - 4q^{12} + 32q^{13} + 8q^{14} - 6q^{15} + 28q^{16} + 4q^{17} - 6q^{19} - 12q^{20} + 44q^{22} - 2q^{23} + 62q^{25} + 2q^{27} - 6q^{28} - 2q^{29} + 4q^{30} + 52q^{31} - 130q^{32} + 6q^{33} + 130q^{34} + 2q^{35} - 26q^{36} - 138q^{38} - 2q^{39} + 24q^{40} + 12q^{41} - 260q^{42} + 11q^{43} - 6q^{45} - 12q^{48} + 140q^{49} - 8q^{51} - 120q^{52} + 86q^{53} - 102q^{55} + 12q^{56} + 52q^{58} - 410q^{59} - 104q^{60} - 15q^{61} - 114q^{62} - 3q^{63} - 6q^{65} + 112q^{66} - 67q^{67} + 106q^{68} + 10q^{69} - 138q^{71} - 64q^{74} + 15q^{75} - 40q^{76} - 44q^{77} - 130q^{78} + 46q^{79} + 24q^{80} + 29q^{81} - 110q^{82} - 6q^{84} - 78q^{85} - 156q^{86} + 94q^{87} - 496q^{88} - 12q^{89} - 8q^{90} + 113q^{91} + 80q^{92} - 3q^{93} - 38q^{94} - 200q^{95} - 147q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(507, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
507.2.t.a $$336$$ $$4.048$$ None $$0$$ $$14$$ $$0$$ $$0$$
507.2.t.b $$360$$ $$4.048$$ None $$0$$ $$-15$$ $$0$$ $$3$$

## Decomposition of $$S_{2}^{\mathrm{old}}(507, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(507, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 2}$$