# Properties

 Label 1728.2.bc Level $1728$ Weight $2$ Character orbit 1728.bc Rep. character $\chi_{1728}(145,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $88$ Newform subspaces $5$ Sturm bound $576$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1728 = 2^{6} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1728.bc (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$144$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$5$$ Sturm bound: $$576$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1728, [\chi])$$.

Total New Old
Modular forms 1248 104 1144
Cusp forms 1056 88 968
Eisenstein series 192 16 176

## Trace form

 $$88q + 2q^{5} + O(q^{10})$$ $$88q + 2q^{5} - 2q^{11} - 2q^{13} + 16q^{17} + 8q^{19} + 2q^{29} + 4q^{31} - 28q^{35} - 8q^{37} + 2q^{43} - 44q^{47} + 16q^{49} + 8q^{53} + 10q^{59} - 2q^{61} + 4q^{65} + 2q^{67} + 30q^{77} + 4q^{79} - 22q^{83} - 12q^{85} + 36q^{91} + 60q^{95} - 4q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1728, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1728.2.bc.a $$4$$ $$13.798$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$-6$$ $$q+(-2\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+(-2-\zeta_{12}+\cdots)q^{7}+\cdots$$
1728.2.bc.b $$4$$ $$13.798$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$12$$ $$q+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+(4-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{7}+\cdots$$
1728.2.bc.c $$4$$ $$13.798$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$4$$ $$-12$$ $$q+(1+\zeta_{12}-\zeta_{12}^{3})q^{5}+(-4-\zeta_{12}+\cdots)q^{7}+\cdots$$
1728.2.bc.d $$4$$ $$13.798$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$8$$ $$6$$ $$q+(2+2\zeta_{12}-2\zeta_{12}^{3})q^{5}+(2-\zeta_{12}+\cdots)q^{7}+\cdots$$
1728.2.bc.e $$72$$ $$13.798$$ None $$0$$ $$0$$ $$-4$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1728, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1728, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(432, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$