# Properties

 Label 273.2.p Level $273$ Weight $2$ Character orbit 273.p Rep. character $\chi_{273}(34,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $40$ Newform subspaces $6$ Sturm bound $74$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.p (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$74$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$5$$

## Dimensions

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

Total New Old
Modular forms 80 40 40
Cusp forms 64 40 24
Eisenstein series 16 0 16

## Trace form

 $$40q + 4q^{7} - 40q^{9} + O(q^{10})$$ $$40q + 4q^{7} - 40q^{9} + 16q^{11} - 24q^{14} - 64q^{16} + 12q^{21} + 16q^{22} + 4q^{28} + 8q^{29} + 40q^{32} - 16q^{35} - 24q^{39} - 24q^{42} + 16q^{44} - 8q^{46} + 40q^{50} - 56q^{53} + 40q^{57} + 48q^{58} - 16q^{60} - 4q^{63} + 16q^{65} - 56q^{67} - 16q^{70} + 24q^{71} - 32q^{74} + 32q^{78} + 24q^{79} + 40q^{81} + 36q^{84} - 40q^{85} + 48q^{86} + 36q^{91} + 176q^{92} + 40q^{93} + 120q^{98} - 16q^{99} + O(q^{100})$$

## 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.p.a $$4$$ $$2.180$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$-8$$ $$4$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-2+2\beta _{2}+\cdots)q^{5}+\cdots$$
273.2.p.b $$4$$ $$2.180$$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$0$$ $$-4$$ $$-4$$ $$q-\beta _{2}q^{3}+2\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
273.2.p.c $$4$$ $$2.180$$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$0$$ $$4$$ $$-4$$ $$q-\beta _{2}q^{3}-2\beta _{2}q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots$$
273.2.p.d $$4$$ $$2.180$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(2-2\beta _{2}+\cdots)q^{5}+\cdots$$
273.2.p.e $$12$$ $$2.180$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$-12$$ $$12$$ $$q+\beta _{8}q^{2}-\beta _{4}q^{3}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+\cdots$$
273.2.p.f $$12$$ $$2.180$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$12$$ $$-4$$ $$q+\beta _{8}q^{2}+\beta _{4}q^{3}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+\cdots$$

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

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