Properties

 Label 228.3.l Level $228$ Weight $3$ Character orbit 228.l Rep. character $\chi_{228}(145,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $4$ Sturm bound $120$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$228 = 2^{2} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 228.l (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$120$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$7$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(228, [\chi])$$.

Total New Old
Modular forms 172 12 160
Cusp forms 148 12 136
Eisenstein series 24 0 24

Trace form

 $$12 q + 2 q^{5} + 20 q^{7} + 18 q^{9} + O(q^{10})$$ $$12 q + 2 q^{5} + 20 q^{7} + 18 q^{9} - 4 q^{11} + 6 q^{13} - 18 q^{15} - 4 q^{17} + 40 q^{19} + 14 q^{23} + 26 q^{25} + 156 q^{29} + 54 q^{33} + 82 q^{35} - 72 q^{39} - 72 q^{41} + 6 q^{43} + 12 q^{45} - 28 q^{47} - 240 q^{49} - 6 q^{53} - 124 q^{55} + 96 q^{57} - 318 q^{59} + 38 q^{61} + 30 q^{63} + 282 q^{67} - 54 q^{73} - 428 q^{77} - 42 q^{79} - 54 q^{81} + 8 q^{83} - 136 q^{85} - 144 q^{87} - 6 q^{89} - 18 q^{91} - 60 q^{93} + 50 q^{95} - 144 q^{97} - 6 q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(228, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
228.3.l.a $2$ $6.213$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$-6$$ $$-10$$ $$q+(1+\zeta_{6})q^{3}+(-6+6\zeta_{6})q^{5}-5q^{7}+\cdots$$
228.3.l.b $2$ $6.213$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$2$$ $$-2$$ $$q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}+\cdots$$
228.3.l.c $2$ $6.213$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$2$$ $$22$$ $$q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}+11q^{7}+\cdots$$
228.3.l.d $6$ $6.213$ 6.0.954288.1 None $$0$$ $$-9$$ $$4$$ $$10$$ $$q+(-1-\beta _{2})q^{3}+(2-2\beta _{2}+\beta _{3}-\beta _{5})q^{5}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(228, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(228, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 2}$$