# Properties

 Label 112.2.i Level $112$ Weight $2$ Character orbit 112.i Rep. character $\chi_{112}(65,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $6$ Newform subspaces $3$ Sturm bound $32$ Trace bound $3$

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## Defining parameters

 Level: $$N$$ $$=$$ $$112 = 2^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 112.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ Sturm bound: $$32$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(112, [\chi])$$.

Total New Old
Modular forms 44 10 34
Cusp forms 20 6 14
Eisenstein series 24 4 20

## Trace form

 $$6 q + 3 q^{3} - q^{5} + 4 q^{7} - 2 q^{9} + O(q^{10})$$ $$6 q + 3 q^{3} - q^{5} + 4 q^{7} - 2 q^{9} - q^{11} - 4 q^{13} - 2 q^{15} - q^{17} + 5 q^{19} - 3 q^{21} - 7 q^{23} + 4 q^{25} - 18 q^{27} - 20 q^{29} - 13 q^{31} + 9 q^{33} - 21 q^{35} + 3 q^{37} + 14 q^{39} - 12 q^{41} + 24 q^{43} + 10 q^{45} - 3 q^{47} + 6 q^{49} + 17 q^{51} + 7 q^{53} + 22 q^{55} + 26 q^{57} + 27 q^{59} + 3 q^{61} + 38 q^{63} - 10 q^{65} - 5 q^{67} + 2 q^{69} - 32 q^{71} - 13 q^{73} - 4 q^{75} + 17 q^{77} - 23 q^{79} - 11 q^{81} - 40 q^{83} + 22 q^{85} - 26 q^{87} - 13 q^{89} - 24 q^{91} + 5 q^{93} - 9 q^{95} - 12 q^{97} + 12 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(112, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.2.i.a $2$ $0.894$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$1$$ $$4$$ $$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
112.2.i.b $2$ $0.894$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-3$$ $$4$$ $$q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
112.2.i.c $2$ $0.894$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$1$$ $$-4$$ $$q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(112, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(112, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 2}$$