# Properties

 Label 273.2.cd Level $273$ Weight $2$ Character orbit 273.cd Rep. character $\chi_{273}(44,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $136$ Newform subspaces $5$ Sturm bound $74$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.cd (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$5$$ Sturm bound: $$74$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$2$$, $$5$$, $$19$$

## Dimensions

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

Total New Old
Modular forms 168 168 0
Cusp forms 136 136 0
Eisenstein series 32 32 0

## Trace form

 $$136 q - 4 q^{3} - 16 q^{6} - 2 q^{7} - 4 q^{9} + O(q^{10})$$ $$136 q - 4 q^{3} - 16 q^{6} - 2 q^{7} - 4 q^{9} - 16 q^{13} - 12 q^{15} + 48 q^{16} - 26 q^{18} - 6 q^{19} - 6 q^{21} - 32 q^{22} + 20 q^{24} - 40 q^{27} - 36 q^{28} - 14 q^{31} - 16 q^{33} + 48 q^{34} - 6 q^{37} - 32 q^{39} - 112 q^{40} - 40 q^{42} - 2 q^{45} + 24 q^{46} + 56 q^{48} - 16 q^{52} + 14 q^{54} - 16 q^{55} - 44 q^{57} - 28 q^{58} + 44 q^{60} + 8 q^{61} + 32 q^{63} - 4 q^{66} - 2 q^{67} - 44 q^{70} - 26 q^{72} - 38 q^{73} - 8 q^{76} + 40 q^{78} + 48 q^{79} + 36 q^{81} - 158 q^{84} + 80 q^{85} - 56 q^{87} + 26 q^{91} + 4 q^{93} + 32 q^{94} - 126 q^{96} - 4 q^{99} + O(q^{100})$$

## 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.cd.a $4$ $2.180$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots$$
273.2.cd.b $4$ $2.180$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$2$$ $$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots$$
273.2.cd.c $8$ $2.180$ $$\Q(\zeta_{24})$$ None $$0$$ $$4$$ $$-4$$ $$0$$ $$q+\zeta_{24}^{7}q^{2}+(1-\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{4}+\cdots)q^{3}+\cdots$$
273.2.cd.d $8$ $2.180$ $$\Q(\zeta_{24})$$ None $$0$$ $$4$$ $$4$$ $$0$$ $$q+\zeta_{24}^{7}q^{2}+(1+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots$$
273.2.cd.e $112$ $2.180$ None $$0$$ $$-12$$ $$0$$ $$-4$$