# Properties

 Label 144.3.o Level $144$ Weight $3$ Character orbit 144.o Rep. character $\chi_{144}(31,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $24$ Newform subspaces $3$ Sturm bound $72$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 144.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$36$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$72$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(144, [\chi])$$.

Total New Old
Modular forms 108 24 84
Cusp forms 84 24 60
Eisenstein series 24 0 24

## Trace form

 $$24q - 12q^{9} + O(q^{10})$$ $$24q - 12q^{9} + 72q^{17} + 24q^{21} - 60q^{25} + 72q^{29} - 36q^{33} - 36q^{41} - 216q^{45} + 84q^{49} - 144q^{53} - 276q^{57} - 144q^{65} - 144q^{69} - 72q^{73} + 144q^{77} + 540q^{81} + 576q^{89} + 576q^{93} + 180q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(144, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
144.3.o.a $$8$$ $$3.924$$ 8.0.856615824.2 None $$0$$ $$-3$$ $$3$$ $$3$$ $$q+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
144.3.o.b $$8$$ $$3.924$$ 8.0.121550625.1 None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+(\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{1}-\beta _{7})q^{5}+\cdots$$
144.3.o.c $$8$$ $$3.924$$ 8.0.856615824.2 None $$0$$ $$3$$ $$3$$ $$-3$$ $$q+(-\beta _{3}+\beta _{4})q^{3}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(144, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(144, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 3}$$