# Properties

 Label 108.4.i Level $108$ Weight $4$ Character orbit 108.i Rep. character $\chi_{108}(13,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $54$ Newform subspaces $1$ Sturm bound $72$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 108.i (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$27$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$1$$ Sturm bound: $$72$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(108, [\chi])$$.

Total New Old
Modular forms 342 54 288
Cusp forms 306 54 252
Eisenstein series 36 0 36

## Trace form

 $$54 q + 12 q^{5} - 48 q^{9} + O(q^{10})$$ $$54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(108, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.4.i.a $54$ $6.372$ None $$0$$ $$0$$ $$12$$ $$0$$

## Decomposition of $$S_{4}^{\mathrm{old}}(108, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(108, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 2}$$