# Properties

 Label 507.2.x Level $507$ Weight $2$ Character orbit 507.x Rep. character $\chi_{507}(2,\cdot)$ Character field $\Q(\zeta_{156})$ Dimension $2832$ Newform subspaces $2$ Sturm bound $121$ Trace bound $1$

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## Defining parameters

 Level: $$N$$ $$=$$ $$507 = 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 507.x (of order $$156$$ and degree $$48$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$507$$ Character field: $$\Q(\zeta_{156})$$ 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 3024 3024 0
Cusp forms 2832 2832 0
Eisenstein series 192 192 0

## Trace form

 $$2832q - 50q^{3} - 92q^{4} - 50q^{6} - 90q^{7} - 50q^{9} + O(q^{10})$$ $$2832q - 50q^{3} - 92q^{4} - 50q^{6} - 90q^{7} - 50q^{9} - 116q^{10} - 52q^{12} - 112q^{13} - 38q^{15} - 212q^{16} - 56q^{18} - 102q^{19} - 74q^{21} - 48q^{22} + 86q^{24} - 104q^{25} - 32q^{27} - 104q^{28} - 174q^{30} - 98q^{31} - 68q^{33} - 68q^{34} - 16q^{36} - 74q^{37} - 118q^{39} - 96q^{40} - 44q^{42} - 134q^{43} + 98q^{45} - 58q^{48} - 122q^{49} - 52q^{51} - 180q^{52} - 98q^{54} - 324q^{55} - 80q^{57} - 132q^{58} - 96q^{60} - 124q^{61} - 198q^{63} - 104q^{64} + 58q^{66} + 112q^{67} + 26q^{69} + 136q^{70} - 64q^{72} - 42q^{73} - 164q^{75} - 68q^{76} + 28q^{78} - 120q^{79} - 38q^{81} - 340q^{82} - 44q^{84} - 116q^{85} - 34q^{87} + 116q^{88} - 52q^{90} - 114q^{91} + 68q^{93} + 36q^{94} - 406q^{96} - 86q^{97} - 92q^{99} + O(q^{100})$$

## 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.x.a $$48$$ $$4.048$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$10$$
507.2.x.b $$2784$$ $$4.048$$ None $$0$$ $$-50$$ $$0$$ $$-100$$