# Properties

 Label 273.2.by Level $273$ Weight $2$ Character orbit 273.by Rep. character $\chi_{273}(76,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $72$ Newform subspaces $4$ 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.by (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$4$$ 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 168 72 96
Cusp forms 136 72 64
Eisenstein series 32 0 32

## Trace form

 $$72q - 2q^{7} + 36q^{9} + O(q^{10})$$ $$72q - 2q^{7} + 36q^{9} - 16q^{11} + 48q^{14} + 24q^{16} - 10q^{21} - 16q^{22} - 56q^{28} - 8q^{29} - 40q^{32} - 8q^{35} - 28q^{37} + 8q^{39} - 12q^{42} - 12q^{43} - 16q^{44} - 112q^{46} - 30q^{49} + 176q^{50} - 112q^{53} - 180q^{56} + 48q^{57} + 48q^{58} - 104q^{60} - 4q^{63} + 32q^{65} + 16q^{67} - 56q^{70} - 24q^{71} - 16q^{74} - 8q^{78} + 48q^{79} - 36q^{81} + 20q^{84} - 56q^{85} - 48q^{86} + 216q^{88} + 86q^{91} - 80q^{92} + 12q^{93} + 96q^{95} + 36q^{98} + 16q^{99} + O(q^{100})$$

## 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.by.a $$4$$ $$2.180$$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$-2$$ $$-2$$ $$q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
273.2.by.b $$4$$ $$2.180$$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$2$$ $$0$$ $$q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$$
273.2.by.c $$32$$ $$2.180$$ None $$-2$$ $$0$$ $$-2$$ $$-2$$
273.2.by.d $$32$$ $$2.180$$ None $$-2$$ $$0$$ $$2$$ $$2$$

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

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