Properties

 Label 135.2.e Level $135$ Weight $2$ Character orbit 135.e Rep. character $\chi_{135}(46,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $8$ Newform subspaces $2$ Sturm bound $36$ Trace bound $1$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$135 = 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 135.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$36$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(135, [\chi])$$.

Total New Old
Modular forms 48 8 40
Cusp forms 24 8 16
Eisenstein series 24 0 24

Trace form

 $$8 q + 2 q^{2} - 4 q^{4} + 2 q^{5} - 2 q^{7} + O(q^{10})$$ $$8 q + 2 q^{2} - 4 q^{4} + 2 q^{5} - 2 q^{7} - 4 q^{11} - 2 q^{13} - 12 q^{14} - 4 q^{16} - 4 q^{17} - 8 q^{19} + 6 q^{20} + 6 q^{22} + 6 q^{23} - 4 q^{25} + 8 q^{26} + 16 q^{28} - 8 q^{29} - 8 q^{31} + 22 q^{32} - 16 q^{35} + 4 q^{37} - 10 q^{38} - 6 q^{40} - 8 q^{41} - 2 q^{43} + 40 q^{44} + 20 q^{47} + 2 q^{50} + 10 q^{52} + 8 q^{53} + 18 q^{58} - 16 q^{59} - 8 q^{61} - 84 q^{62} - 16 q^{64} + 6 q^{65} - 8 q^{67} - 26 q^{68} + 6 q^{70} + 16 q^{71} - 8 q^{73} - 20 q^{74} + 4 q^{76} + 6 q^{77} + 4 q^{79} - 12 q^{80} - 48 q^{82} - 6 q^{83} + 6 q^{85} + 20 q^{86} + 18 q^{88} + 48 q^{89} + 32 q^{91} + 36 q^{92} + 24 q^{94} + 12 q^{95} + 16 q^{97} + 76 q^{98} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(135, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.2.e.a $2$ $1.078$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-1$$ $$3$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots$$
135.2.e.b $6$ $1.078$ 6.0.954288.1 None $$1$$ $$0$$ $$3$$ $$-5$$ $$q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(135, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(135, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$