Properties

 Label 90.3.g Level $90$ Weight $3$ Character orbit 90.g Rep. character $\chi_{90}(37,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $10$ Newform subspaces $4$ Sturm bound $54$ Trace bound $5$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$90 = 2 \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 90.g (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$54$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$, $$11$$

Dimensions

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

Total New Old
Modular forms 88 10 78
Cusp forms 56 10 46
Eisenstein series 32 0 32

Trace form

 $$10 q - 2 q^{2} + 20 q^{7} + 4 q^{8} + O(q^{10})$$ $$10 q - 2 q^{2} + 20 q^{7} + 4 q^{8} + 22 q^{10} + 32 q^{11} + 6 q^{13} - 40 q^{16} - 58 q^{17} - 28 q^{20} - 16 q^{22} + 20 q^{23} + 14 q^{25} - 12 q^{26} - 40 q^{28} - 152 q^{31} + 8 q^{32} + 92 q^{35} - 126 q^{37} + 104 q^{38} - 4 q^{40} - 16 q^{41} + 108 q^{43} + 136 q^{46} - 60 q^{47} - 142 q^{50} + 12 q^{52} - 206 q^{53} + 144 q^{55} - 80 q^{56} - 8 q^{58} + 96 q^{61} + 184 q^{62} + 234 q^{65} + 284 q^{67} + 116 q^{68} + 184 q^{70} - 8 q^{71} - 62 q^{73} + 16 q^{76} + 160 q^{77} - 232 q^{82} - 228 q^{83} - 514 q^{85} - 264 q^{86} + 32 q^{88} + 120 q^{91} + 40 q^{92} + 136 q^{95} - 222 q^{97} + 206 q^{98} + O(q^{100})$$

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.g.a $2$ $2.452$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$-6$$ $$16$$ $$q+(-1-i)q^{2}+2iq^{4}+(-3+4i)q^{5}+\cdots$$
90.3.g.b $2$ $2.452$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$4$$ $$q+(1+i)q^{2}+2iq^{4}+5iq^{5}+(2+2i)q^{7}+\cdots$$
90.3.g.c $2$ $2.452$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$6$$ $$16$$ $$q+(1+i)q^{2}+2iq^{4}+(3-4i)q^{5}+(8+\cdots)q^{7}+\cdots$$
90.3.g.d $4$ $2.452$ $$\Q(i, \sqrt{6})$$ None $$-4$$ $$0$$ $$0$$ $$-16$$ $$q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(90, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$