Properties

 Label 90.3.k Level $90$ Weight $3$ Character orbit 90.k Rep. character $\chi_{90}(7,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $48$ Newform subspaces $2$ Sturm bound $54$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$90 = 2 \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 90.k (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$54$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$7$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(90, [\chi])$$.

Total New Old
Modular forms 160 48 112
Cusp forms 128 48 80
Eisenstein series 32 0 32

Trace form

 $$48 q + 4 q^{3} + 16 q^{6} + O(q^{10})$$ $$48 q + 4 q^{3} + 16 q^{6} - 24 q^{11} + 8 q^{12} + 4 q^{15} + 96 q^{16} - 72 q^{17} - 32 q^{18} + 24 q^{20} - 32 q^{21} - 120 q^{23} + 12 q^{25} + 172 q^{27} - 96 q^{30} - 116 q^{33} - 576 q^{35} - 80 q^{36} + 168 q^{37} - 72 q^{38} - 160 q^{42} - 28 q^{45} - 48 q^{46} + 12 q^{47} + 32 q^{48} + 96 q^{50} + 488 q^{51} + 768 q^{53} - 264 q^{55} + 48 q^{56} + 340 q^{57} - 48 q^{58} + 88 q^{60} - 96 q^{61} + 288 q^{62} + 4 q^{63} + 408 q^{65} + 160 q^{66} + 156 q^{67} - 72 q^{68} + 48 q^{71} + 128 q^{72} - 652 q^{75} - 96 q^{77} - 504 q^{78} - 64 q^{81} - 96 q^{82} - 624 q^{83} + 96 q^{85} + 432 q^{86} - 584 q^{87} + 112 q^{90} - 336 q^{91} - 240 q^{92} + 760 q^{93} + 696 q^{95} + 32 q^{96} - 396 q^{97} + 288 q^{98} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(90, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
90.3.k.a $24$ $2.452$ None $$-12$$ $$0$$ $$0$$ $$-6$$
90.3.k.b $24$ $2.452$ None $$12$$ $$4$$ $$0$$ $$6$$

Decomposition of $$S_{3}^{\mathrm{old}}(90, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(90, [\chi]) \simeq$$ $$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$