# Properties

 Label 273.2.bt Level $273$ Weight $2$ Character orbit 273.bt Rep. character $\chi_{273}(136,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $76$ Newform subspaces $2$ 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.bt (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ 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 164 76 88
Cusp forms 132 76 56
Eisenstein series 32 0 32

## Trace form

 $$76q + 4q^{7} + 38q^{9} + O(q^{10})$$ $$76q + 4q^{7} + 38q^{9} - 16q^{11} + 8q^{12} + 24q^{14} - 88q^{16} - 32q^{19} - 12q^{21} + 8q^{22} + 36q^{24} - 60q^{26} + 32q^{28} + 16q^{29} - 2q^{31} - 40q^{32} - 8q^{35} - 2q^{37} - 26q^{39} - 60q^{40} + 36q^{41} - 12q^{42} - 36q^{43} + 56q^{44} + 8q^{46} + 44q^{49} - 40q^{50} - 24q^{51} + 44q^{52} - 16q^{53} + 12q^{55} - 72q^{56} - 38q^{57} + 24q^{58} - 96q^{59} + 28q^{60} - 72q^{61} - 72q^{62} + 2q^{63} - 88q^{65} + 112q^{70} + 36q^{71} - 46q^{73} + 80q^{74} + 28q^{75} + 76q^{76} - 8q^{78} + 204q^{80} - 38q^{81} + 48q^{82} - 48q^{83} + 20q^{84} + 4q^{85} + 24q^{86} + 48q^{89} - 60q^{91} + 136q^{92} + 34q^{93} - 36q^{94} + 72q^{96} + 98q^{97} - 36q^{98} - 8q^{99} + O(q^{100})$$

## 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.bt.a $$36$$ $$2.180$$ None $$0$$ $$0$$ $$0$$ $$6$$
273.2.bt.b $$40$$ $$2.180$$ None $$0$$ $$0$$ $$0$$ $$-2$$

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

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