# Properties

 Label 273.2.bd Level $273$ Weight $2$ Character orbit 273.bd Rep. character $\chi_{273}(43,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $2$ Sturm bound $74$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.bd (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$74$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 84 32 52
Cusp forms 68 32 36
Eisenstein series 16 0 16

## Trace form

 $$32 q + 20 q^{4} - 16 q^{9} + O(q^{10})$$ $$32 q + 20 q^{4} - 16 q^{9} - 8 q^{10} - 12 q^{11} + 16 q^{12} - 8 q^{13} - 12 q^{15} - 20 q^{16} + 8 q^{17} + 24 q^{20} - 20 q^{22} - 8 q^{23} - 8 q^{25} + 40 q^{26} + 12 q^{33} + 4 q^{35} + 20 q^{36} + 12 q^{37} - 56 q^{38} - 8 q^{39} - 88 q^{40} - 12 q^{41} - 4 q^{42} + 4 q^{43} - 12 q^{45} - 12 q^{46} + 16 q^{49} + 60 q^{50} - 24 q^{51} + 4 q^{52} + 40 q^{53} + 12 q^{55} + 12 q^{58} - 84 q^{59} - 4 q^{61} - 4 q^{62} - 32 q^{64} - 64 q^{65} - 32 q^{66} + 12 q^{67} + 16 q^{68} + 4 q^{69} + 24 q^{74} - 16 q^{75} + 48 q^{76} + 16 q^{77} + 24 q^{78} + 88 q^{79} + 144 q^{80} - 16 q^{81} - 60 q^{82} + 24 q^{85} + 24 q^{87} + 60 q^{88} + 96 q^{89} + 16 q^{90} - 8 q^{91} - 136 q^{92} - 8 q^{94} - 28 q^{95} - 60 q^{97} + O(q^{100})$$

## 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.bd.a $16$ $2.180$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$-8$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(-1+\beta _{12})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots$$
273.2.bd.b $16$ $2.180$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$8$$ $$0$$ $$0$$ $$q-\beta _{14}q^{2}-\beta _{5}q^{3}+(2+2\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(273, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 2}$$