# Properties

 Label 273.2.bl Level $273$ Weight $2$ Character orbit 273.bl Rep. character $\chi_{273}(88,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $38$ Newform subspaces $4$ Sturm bound $74$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.bl (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$74$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(273, [\chi])$$.

Total New Old
Modular forms 82 38 44
Cusp forms 66 38 28
Eisenstein series 16 0 16

## Trace form

 $$38q - 6q^{3} + 20q^{4} - q^{7} + 38q^{9} + O(q^{10})$$ $$38q - 6q^{3} + 20q^{4} - q^{7} + 38q^{9} + 16q^{10} - 8q^{12} - 2q^{13} - 24q^{14} - 14q^{16} - 4q^{17} - 24q^{20} + 7q^{21} + 10q^{22} + 4q^{23} + 25q^{25} + 22q^{26} - 6q^{27} - 44q^{28} + 3q^{31} - 14q^{35} + 20q^{36} - 15q^{37} + 16q^{38} - 8q^{39} + 14q^{40} + 18q^{41} - 22q^{42} + 4q^{43} - 12q^{44} + 12q^{46} - 36q^{47} + 18q^{48} - 29q^{49} - 102q^{50} - 44q^{52} - 8q^{53} + 30q^{55} - 6q^{56} - 48q^{59} - 36q^{60} - 34q^{61} - 40q^{62} - q^{63} - 20q^{64} + 8q^{65} + 16q^{66} - 8q^{68} - 20q^{69} - 36q^{70} + 18q^{71} + 42q^{73} + 12q^{74} - 13q^{75} + 58q^{77} - 18q^{78} + 19q^{79} + 38q^{81} - 12q^{82} + 50q^{84} - 48q^{85} - 36q^{86} + 18q^{87} + 24q^{88} - 48q^{89} + 16q^{90} + 29q^{91} + 140q^{92} + 3q^{93} - 104q^{94} + 20q^{95} + 30q^{96} + 27q^{97} - 30q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(273, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
273.2.bl.a $$2$$ $$2.180$$ $$\Q(\sqrt{-3})$$ None $$3$$ $$-2$$ $$6$$ $$1$$ $$q+(2-\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+(2+\cdots)q^{5}+\cdots$$
273.2.bl.b $$4$$ $$2.180$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$3$$ $$4$$ $$-6$$ $$0$$ $$q+(1-\beta _{3})q^{2}+q^{3}+(\beta _{1}+\beta _{2}-2\beta _{3})q^{4}+\cdots$$
273.2.bl.c $$12$$ $$2.180$$ 12.0.$$\cdots$$.1 None $$-3$$ $$12$$ $$6$$ $$3$$ $$q+(-\beta _{1}-\beta _{6}+\beta _{8})q^{2}+q^{3}+(-1+\cdots)q^{4}+\cdots$$
273.2.bl.d $$20$$ $$2.180$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$-3$$ $$-20$$ $$-6$$ $$-5$$ $$q+\beta _{3}q^{2}-q^{3}+(\beta _{11}+\beta _{17})q^{4}+\beta _{8}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(273, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(273, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 2}$$