# Properties

 Label 90.3.j Level $90$ Weight $3$ Character orbit 90.j Rep. character $\chi_{90}(29,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $24$ Newform subspaces $2$ Sturm bound $54$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$90 = 2 \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 90.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$54$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

## Trace form

 $$24 q - 24 q^{4} + 18 q^{5} - 8 q^{6} + 20 q^{9} + O(q^{10})$$ $$24 q - 24 q^{4} + 18 q^{5} - 8 q^{6} + 20 q^{9} + 36 q^{11} - 36 q^{14} - 26 q^{15} - 48 q^{16} - 36 q^{20} + 112 q^{21} + 8 q^{24} - 6 q^{25} + 36 q^{29} + 4 q^{30} - 60 q^{31} - 104 q^{36} - 348 q^{39} - 144 q^{41} + 242 q^{45} - 24 q^{46} + 108 q^{49} + 288 q^{50} + 64 q^{51} + 260 q^{54} - 156 q^{55} + 72 q^{56} - 36 q^{59} + 20 q^{60} + 48 q^{61} + 192 q^{64} - 414 q^{65} + 272 q^{66} + 236 q^{69} + 48 q^{70} + 144 q^{74} - 370 q^{75} + 132 q^{79} - 824 q^{81} + 8 q^{84} + 48 q^{85} - 432 q^{86} + 112 q^{90} + 168 q^{91} - 84 q^{94} + 540 q^{95} + 16 q^{96} + 52 q^{99} + O(q^{100})$$

## 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.j.a $8$ $2.452$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$-12$$ $$0$$ $$q-\zeta_{24}^{4}q^{2}+3\zeta_{24}q^{3}+(-2+2\zeta_{24}^{2}+\cdots)q^{4}+\cdots$$
90.3.j.b $16$ $2.452$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$30$$ $$0$$ $$q-\beta _{7}q^{2}+\beta _{13}q^{3}+2\beta _{6}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$$

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

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