Properties

 Label 572.2.bb Level $572$ Weight $2$ Character orbit 572.bb Rep. character $\chi_{572}(51,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $320$ Newform subspaces $2$ Sturm bound $168$ Trace bound $1$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$572 = 2^{2} \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 572.bb (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$572$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$168$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(572, [\chi])$$.

Total New Old
Modular forms 352 352 0
Cusp forms 320 320 0
Eisenstein series 32 32 0

Trace form

 $$320q - 6q^{4} + 60q^{9} + O(q^{10})$$ $$320q - 6q^{4} + 60q^{9} - 20q^{12} - 10q^{13} - 6q^{14} - 2q^{16} - 20q^{17} - 54q^{22} + 52q^{25} - 34q^{26} - 20q^{29} - 60q^{30} + 86q^{36} + 26q^{38} - 10q^{40} - 68q^{42} + 4q^{48} + 20q^{49} - 30q^{52} - 4q^{53} - 116q^{56} - 20q^{61} - 10q^{62} - 6q^{64} + 86q^{66} - 140q^{68} + 56q^{69} + 40q^{74} - 44q^{77} - 48q^{78} - 84q^{81} - 70q^{82} - 6q^{88} + 180q^{90} - 2q^{92} - 10q^{94} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(572, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
572.2.bb.a $$16$$ $$4.567$$ 16.0.$$\cdots$$.9 $$\Q(\sqrt{-13})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{8}q^{2}+(2+2\beta _{2}-2\beta _{7}-2\beta _{9})q^{4}+\cdots$$
572.2.bb.b $$304$$ $$4.567$$ None $$0$$ $$0$$ $$0$$ $$0$$