Properties

 Label 228.3.h Level $228$ Weight $3$ Character orbit 228.h Rep. character $\chi_{228}(37,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $1$ Sturm bound $120$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$228 = 2^{2} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 228.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$120$$ Trace bound: $$0$$

Dimensions

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

Total New Old
Modular forms 86 6 80
Cusp forms 74 6 68
Eisenstein series 12 0 12

Trace form

 $$6 q - 2 q^{5} - 2 q^{7} - 18 q^{9} + O(q^{10})$$ $$6 q - 2 q^{5} - 2 q^{7} - 18 q^{9} - 26 q^{11} - 50 q^{17} - 10 q^{19} + 28 q^{23} + 28 q^{25} + 2 q^{35} + 72 q^{39} - 210 q^{43} + 6 q^{45} + 22 q^{47} - 36 q^{49} + 10 q^{55} + 48 q^{57} + 214 q^{61} + 6 q^{63} + 102 q^{73} + 266 q^{77} + 54 q^{81} - 404 q^{83} + 370 q^{85} - 144 q^{87} - 120 q^{93} + 358 q^{95} + 78 q^{99} + O(q^{100})$$

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.h.a $6$ $6.213$ 6.0.219615408.1 None $$0$$ $$0$$ $$-2$$ $$-2$$ $$q+\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}-3q^{9}+(-4+\cdots)q^{11}+\cdots$$

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

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