# Properties

 Label 273.2.n Level $273$ Weight $2$ Character orbit 273.n Rep. character $\chi_{273}(8,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $56$ Newform subspaces $3$ Sturm bound $74$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.n (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$39$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$74$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 80 56 24
Cusp forms 64 56 8
Eisenstein series 16 0 16

## Trace form

 $$56q + 12q^{6} + O(q^{10})$$ $$56q + 12q^{6} + 8q^{13} - 4q^{15} - 40q^{16} - 20q^{18} + 8q^{19} + 4q^{21} + 16q^{22} - 8q^{24} - 24q^{27} - 16q^{31} + 36q^{33} - 48q^{37} - 8q^{39} + 16q^{40} + 28q^{45} - 24q^{46} + 48q^{48} - 72q^{52} + 36q^{54} - 96q^{55} - 32q^{57} + 24q^{58} + 44q^{60} - 96q^{61} + 8q^{63} - 136q^{66} + 40q^{67} + 24q^{70} + 32q^{72} + 16q^{73} + 104q^{76} - 68q^{78} + 32q^{79} + 56q^{81} + 12q^{84} - 32q^{85} - 48q^{87} + 8q^{91} - 20q^{93} + 96q^{94} + 8q^{96} - 96q^{97} - 12q^{99} + O(q^{100})$$

## 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.n.a $$4$$ $$2.180$$ $$\Q(\zeta_{8})$$ None $$-4$$ $$-4$$ $$-8$$ $$0$$ $$q+(-1-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$$
273.2.n.b $$4$$ $$2.180$$ $$\Q(\zeta_{8})$$ None $$4$$ $$-4$$ $$8$$ $$0$$ $$q+(1-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots$$
273.2.n.c $$48$$ $$2.180$$ None $$0$$ $$8$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(273, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 2}$$