# Properties

 Label 108.4.e Level $108$ Weight $4$ Character orbit 108.e Rep. character $\chi_{108}(37,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $6$ 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.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ 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 126 6 120
Cusp forms 90 6 84
Eisenstein series 36 0 36

## Trace form

 $$6 q - 6 q^{5} - 6 q^{7} + O(q^{10})$$ $$6 q - 6 q^{5} - 6 q^{7} - 51 q^{11} + 12 q^{13} + 222 q^{17} + 30 q^{19} - 210 q^{23} - 3 q^{25} - 456 q^{29} + 48 q^{31} + 1104 q^{35} - 96 q^{37} - 897 q^{41} + 129 q^{43} - 522 q^{47} - 225 q^{49} + 2208 q^{53} - 216 q^{55} - 453 q^{59} - 402 q^{61} - 1110 q^{65} - 213 q^{67} - 120 q^{71} + 750 q^{73} - 1128 q^{77} + 552 q^{79} + 612 q^{83} + 1188 q^{85} + 924 q^{89} - 264 q^{91} + 2184 q^{95} + 93 q^{97} + O(q^{100})$$

## 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.e.a $6$ $6.372$ 6.0.6831243.2 None $$0$$ $$0$$ $$-6$$ $$-6$$ $$q+(-2+2\beta _{1}+\beta _{5})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$

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

$$S_{4}^{\mathrm{old}}(108, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 2}$$