# Properties

 Label 215.2.r Level 215 Weight 2 Character orbit r Rep. character $$\chi_{215}(2,\cdot)$$ Character field $$\Q(\zeta_{28})$$ Dimension 240 Newform subspaces 1 Sturm bound 44 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$215 = 5 \cdot 43$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 215.r (of order $$28$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$215$$ Character field: $$\Q(\zeta_{28})$$ Newform subspaces: $$1$$ Sturm bound: $$44$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(215, [\chi])$$.

Total New Old
Modular forms 288 288 0
Cusp forms 240 240 0
Eisenstein series 48 48 0

## Trace form

 $$240q - 14q^{2} - 14q^{3} - 14q^{5} - 40q^{6} - 14q^{8} + O(q^{10})$$ $$240q - 14q^{2} - 14q^{3} - 14q^{5} - 40q^{6} - 14q^{8} + 6q^{10} - 20q^{11} - 42q^{12} + 10q^{13} - 10q^{15} + 48q^{16} - 6q^{17} - 56q^{18} - 14q^{20} - 36q^{21} - 14q^{22} + 14q^{23} - 6q^{25} - 28q^{26} - 14q^{27} - 70q^{28} - 224q^{30} - 36q^{31} + 126q^{32} + 14q^{33} - 38q^{35} + 64q^{36} + 98q^{38} - 82q^{40} - 36q^{41} + 112q^{43} - 14q^{45} - 28q^{46} - 42q^{47} + 14q^{48} + 196q^{51} - 22q^{52} - 22q^{53} - 14q^{55} - 56q^{56} + 22q^{57} - 30q^{58} + 86q^{60} - 28q^{61} + 70q^{62} - 112q^{63} - 98q^{65} - 256q^{66} - 90q^{67} - 138q^{68} + 126q^{70} - 28q^{71} + 14q^{72} + 112q^{73} - 14q^{75} - 28q^{76} + 154q^{77} + 34q^{78} + 120q^{81} + 182q^{82} - 10q^{83} + 72q^{86} + 152q^{87} + 14q^{88} - 110q^{90} - 28q^{91} + 84q^{92} + 26q^{95} - 272q^{96} + 50q^{97} - 84q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(215, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
215.2.r.a $$240$$ $$1.717$$ None $$-14$$ $$-14$$ $$-14$$ $$0$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database