# Properties

 Label 273.2.bw Level $273$ Weight $2$ Character orbit 273.bw Rep. character $\chi_{273}(11,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $132$ 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.bw (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ 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 164 164 0
Cusp forms 132 132 0
Eisenstein series 32 32 0

## Trace form

 $$132 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 4 q^{9} + O(q^{10})$$ $$132 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 4 q^{9} - 36 q^{12} - 16 q^{13} - 6 q^{15} + 40 q^{16} + 22 q^{18} - 14 q^{19} - 24 q^{21} - 8 q^{22} - 4 q^{24} - 40 q^{27} - 72 q^{28} - 12 q^{31} + 50 q^{33} - 48 q^{34} - 60 q^{36} + 8 q^{37} + 16 q^{39} + 44 q^{40} + 44 q^{42} - 108 q^{43} + 58 q^{45} + 48 q^{46} - 64 q^{48} + 2 q^{49} + 36 q^{51} - 20 q^{52} - 22 q^{54} - 16 q^{55} + 10 q^{57} - 28 q^{58} - 4 q^{60} - 40 q^{61} + 20 q^{63} - 34 q^{66} + 74 q^{67} - 54 q^{69} + 64 q^{70} - 98 q^{72} + 62 q^{73} - 42 q^{75} + 116 q^{76} + 82 q^{78} - 24 q^{79} - 12 q^{81} + 4 q^{84} + 56 q^{85} - 2 q^{87} - 22 q^{91} + 16 q^{93} + 32 q^{94} - 54 q^{96} + 62 q^{97} - 10 q^{99} + O(q^{100})$$

## 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.bw.a $4$ $2.180$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{4}+\cdots$$
273.2.bw.b $128$ $2.180$ None $$0$$ $$-4$$ $$0$$ $$-16$$