# Properties

 Label 144.3.g Level $144$ Weight $3$ Character orbit 144.g Rep. character $\chi_{144}(127,\cdot)$ Character field $\Q$ Dimension $5$ Newform subspaces $3$ Sturm bound $72$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 144.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$72$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 60 5 55
Cusp forms 36 5 31
Eisenstein series 24 0 24

## Trace form

 $$5q - 6q^{5} + O(q^{10})$$ $$5q - 6q^{5} + 26q^{13} + 42q^{17} - 17q^{25} - 102q^{29} + 34q^{37} + 90q^{41} - 235q^{49} - 54q^{53} - 14q^{61} + 228q^{65} + 146q^{73} - 288q^{77} + 108q^{85} - 150q^{89} + 194q^{97} + O(q^{100})$$

## 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.g.a $$1$$ $$3.924$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$6$$ $$0$$ $$q+6q^{5}+10q^{13}+30q^{17}+11q^{25}+\cdots$$
144.3.g.b $$2$$ $$3.924$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-12$$ $$0$$ $$q-6q^{5}-\zeta_{6}q^{7}-3\zeta_{6}q^{11}-14q^{13}+\cdots$$
144.3.g.c $$2$$ $$3.924$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{7}+22q^{13}-2\zeta_{6}q^{19}-5^{2}q^{25}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(144, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$