# Properties

 Label 108.4.h Level $108$ Weight $4$ Character orbit 108.h Rep. character $\chi_{108}(35,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $2$ Sturm bound $72$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 108.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$36$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$72$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 120 40 80
Cusp forms 96 32 64
Eisenstein series 24 8 16

## Trace form

 $$32 q + 3 q^{2} - q^{4} + 6 q^{5} + O(q^{10})$$ $$32 q + 3 q^{2} - q^{4} + 6 q^{5} - 20 q^{10} - 2 q^{13} + 78 q^{14} - q^{16} + 234 q^{20} + 15 q^{22} + 198 q^{25} - 132 q^{28} - 78 q^{29} - 687 q^{32} - 191 q^{34} - 8 q^{37} - 891 q^{38} + 34 q^{40} + 156 q^{41} + 48 q^{46} + 194 q^{49} + 1977 q^{50} - 332 q^{52} + 3006 q^{56} - 314 q^{58} - 2 q^{61} + 410 q^{64} - 690 q^{65} - 4845 q^{68} + 84 q^{70} - 836 q^{73} - 5874 q^{74} - 495 q^{76} - 978 q^{77} + 682 q^{82} + 248 q^{85} + 8331 q^{86} + 531 q^{88} + 8724 q^{92} + 168 q^{94} + 16 q^{97} + O(q^{100})$$

## 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.h.a $8$ $6.372$ 8.0.$$\cdots$$.1 None $$3$$ $$0$$ $$-66$$ $$0$$ $$q+\beta _{7}q^{2}+(2\beta _{2}-2\beta _{3}-2\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$$
108.4.h.b $24$ $6.372$ None $$0$$ $$0$$ $$72$$ $$0$$

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

$$S_{4}^{\mathrm{old}}(108, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 2}$$