# Properties

 Label 144.2.k Level $144$ Weight $2$ Character orbit 144.k Rep. character $\chi_{144}(37,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $18$ Newform subspaces $3$ Sturm bound $48$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 144.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(144, [\chi])$$.

Total New Old
Modular forms 56 22 34
Cusp forms 40 18 22
Eisenstein series 16 4 12

## Trace form

 $$18 q + 2 q^{2} + 2 q^{5} + 8 q^{8} + O(q^{10})$$ $$18 q + 2 q^{2} + 2 q^{5} + 8 q^{8} + 8 q^{10} + 6 q^{11} - 2 q^{13} - 8 q^{14} - 8 q^{16} + 4 q^{17} - 10 q^{19} - 20 q^{20} - 8 q^{22} - 24 q^{26} - 16 q^{28} + 10 q^{29} - 16 q^{31} - 8 q^{32} - 36 q^{34} - 20 q^{35} + 6 q^{37} + 20 q^{38} - 16 q^{40} - 22 q^{43} + 44 q^{44} + 36 q^{46} - 16 q^{47} - 10 q^{49} + 42 q^{50} + 36 q^{52} - 6 q^{53} + 8 q^{56} + 12 q^{58} - 26 q^{59} + 14 q^{61} - 4 q^{62} + 48 q^{64} + 12 q^{65} + 6 q^{67} - 32 q^{68} + 32 q^{70} - 52 q^{74} - 36 q^{76} - 20 q^{77} + 32 q^{79} - 16 q^{80} + 42 q^{83} - 28 q^{85} + 16 q^{86} + 24 q^{88} + 52 q^{91} + 40 q^{92} + 8 q^{94} + 60 q^{95} - 4 q^{97} + 46 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(144, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.2.k.a $2$ $1.150$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$2$$ $$0$$ $$q+(1+i)q^{2}+2iq^{4}+(1+i)q^{5}-2iq^{7}+\cdots$$
144.2.k.b $8$ $1.150$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+(-1-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$$
144.2.k.c $8$ $1.150$ 8.0.629407744.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{4}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(144, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(144, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$