# Properties

 Label 268.2.e Level 268 Weight 2 Character orbit e Rep. character $$\chi_{268}(29,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 12 Newforms 1 Sturm bound 68 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$268 = 2^{2} \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 268.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$67$$ Character field: $$\Q(\zeta_{3})$$ Newforms: $$1$$ Sturm bound: $$68$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(268, [\chi])$$.

Total New Old
Modular forms 74 12 62
Cusp forms 62 12 50
Eisenstein series 12 0 12

## Trace form

 $$12q - 4q^{3} + 6q^{5} - 3q^{7} + 4q^{9} + O(q^{10})$$ $$12q - 4q^{3} + 6q^{5} - 3q^{7} + 4q^{9} - 5q^{11} + q^{13} + 2q^{15} + 3q^{17} + 3q^{19} - 6q^{21} + 5q^{23} + 26q^{25} + 2q^{27} + 9q^{29} - q^{31} + 2q^{33} - q^{35} - 10q^{37} - 17q^{39} - 11q^{41} - 28q^{43} + 6q^{45} - 4q^{47} - q^{49} - 26q^{51} - 12q^{53} - 4q^{55} - 14q^{57} - 6q^{59} - 21q^{61} + 5q^{63} - 18q^{67} - 13q^{69} + 16q^{71} + 11q^{73} + 26q^{75} + 34q^{77} - q^{79} - 12q^{81} + q^{83} - 2q^{85} - 21q^{87} + 56q^{89} - 58q^{91} + 5q^{93} + 39q^{95} - 31q^{97} - 16q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(268, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
268.2.e.a $$12$$ $$2.140$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-4$$ $$6$$ $$-3$$ $$q+\beta _{2}q^{3}-\beta _{8}q^{5}+(\beta _{6}-\beta _{7})q^{7}+\beta _{3}q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(268, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(268, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(67, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(134, [\chi])$$$$^{\oplus 2}$$