# Properties

 Label 273.2.c Level $273$ Weight $2$ Character orbit 273.c Rep. character $\chi_{273}(64,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $3$ 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.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$3$$ 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 40 16 24
Cusp forms 32 16 16
Eisenstein series 8 0 8

## Trace form

 $$16 q - 20 q^{4} + 16 q^{9} + O(q^{10})$$ $$16 q - 20 q^{4} + 16 q^{9} + 8 q^{10} + 8 q^{12} - 4 q^{13} + 20 q^{16} + 16 q^{17} - 40 q^{22} - 4 q^{23} - 52 q^{25} + 20 q^{26} - 12 q^{29} - 4 q^{35} - 20 q^{36} + 56 q^{38} + 8 q^{39} + 16 q^{40} + 4 q^{42} + 20 q^{43} - 48 q^{48} - 16 q^{49} - 24 q^{51} + 20 q^{52} - 28 q^{53} - 8 q^{61} - 56 q^{62} + 20 q^{64} + 28 q^{65} + 8 q^{66} - 40 q^{68} + 8 q^{69} + 96 q^{74} + 16 q^{75} - 16 q^{77} - 36 q^{78} - 4 q^{79} + 16 q^{81} + 24 q^{87} + 24 q^{88} + 8 q^{90} - 4 q^{91} + 16 q^{92} - 64 q^{94} - 68 q^{95} + O(q^{100})$$

## 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.c.a $2$ $2.180$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+2iq^{2}+q^{3}-2q^{4}+3iq^{5}+2iq^{6}+\cdots$$
273.2.c.b $6$ $2.180$ 6.0.350464.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+q^{3}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$$
273.2.c.c $8$ $2.180$ 8.0.$$\cdots$$.1 None $$0$$ $$-8$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-q^{3}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$$

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

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