# Properties

 Label 55.6.e Level $55$ Weight $6$ Character orbit 55.e Rep. character $\chi_{55}(32,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $56$ Newform subspaces $2$ Sturm bound $36$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$55 = 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 55.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$36$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(55, [\chi])$$.

Total New Old
Modular forms 64 64 0
Cusp forms 56 56 0
Eisenstein series 8 8 0

## Trace form

 $$56 q - 6 q^{3} - 48 q^{5} + O(q^{10})$$ $$56 q - 6 q^{3} - 48 q^{5} - 364 q^{11} + 2808 q^{12} + 1116 q^{15} - 10512 q^{16} + 14624 q^{20} + 2680 q^{22} - 2106 q^{23} - 6246 q^{25} + 2432 q^{26} + 4326 q^{27} + 9672 q^{31} + 27914 q^{33} - 117672 q^{36} + 21618 q^{37} + 4400 q^{38} - 43480 q^{42} + 22718 q^{45} + 5268 q^{47} + 89904 q^{48} + 5984 q^{53} - 18106 q^{55} + 304264 q^{56} - 220200 q^{58} - 173264 q^{60} + 207000 q^{66} - 163722 q^{67} - 216880 q^{70} + 20612 q^{71} + 203556 q^{75} - 341160 q^{77} + 15160 q^{78} + 616192 q^{80} - 203292 q^{81} + 349720 q^{82} - 94768 q^{86} + 539000 q^{88} - 864768 q^{91} + 179288 q^{92} - 33002 q^{93} - 306762 q^{97} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(55, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.6.e.a $4$ $8.821$ $$\Q(i, \sqrt{11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$-62$$ $$0$$ $$0$$ $$q+(-15+\beta _{1}-2^{4}\beta _{2}+\beta _{3})q^{3}-2^{5}\beta _{2}q^{4}+\cdots$$
55.6.e.b $52$ $8.821$ None $$0$$ $$56$$ $$-48$$ $$0$$