# Properties

 Label 324.4.i Level $324$ Weight $4$ Character orbit 324.i Rep. character $\chi_{324}(37,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $54$ Newform subspaces $1$ Sturm bound $216$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$324 = 2^{2} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 324.i (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$27$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$1$$ Sturm bound: $$216$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(324, [\chi])$$.

Total New Old
Modular forms 1026 54 972
Cusp forms 918 54 864
Eisenstein series 108 0 108

## Trace form

 $$54q - 12q^{5} + O(q^{10})$$ $$54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(324, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
324.4.i.a $$54$$ $$19.117$$ None $$0$$ $$0$$ $$-12$$ $$0$$

## Decomposition of $$S_{4}^{\mathrm{old}}(324, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(324, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(162, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database