# Properties

 Label 112.6.i Level $112$ Weight $6$ Character orbit 112.i Rep. character $\chi_{112}(65,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $38$ Newform subspaces $7$ Sturm bound $96$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$112 = 2^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 112.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$7$$ Sturm bound: $$96$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(112, [\chi])$$.

Total New Old
Modular forms 172 42 130
Cusp forms 148 38 110
Eisenstein series 24 4 20

## Trace form

 $$38 q + 19 q^{3} - q^{5} - 60 q^{7} - 1378 q^{9} + O(q^{10})$$ $$38 q + 19 q^{3} - q^{5} - 60 q^{7} - 1378 q^{9} + 303 q^{11} - 4 q^{13} - 482 q^{15} - q^{17} + 549 q^{19} - 579 q^{21} + 1497 q^{23} - 8012 q^{25} - 12146 q^{27} + 3884 q^{29} - 3597 q^{31} - 4231 q^{33} + 14859 q^{35} - 5325 q^{37} - 11714 q^{39} - 9644 q^{41} - 20936 q^{43} + 106 q^{45} - 38403 q^{47} + 3750 q^{49} - 33535 q^{51} - 3609 q^{53} + 42166 q^{55} + 28890 q^{57} + 69899 q^{59} - 6285 q^{61} - 96138 q^{63} - 12234 q^{65} - 74741 q^{67} - 21022 q^{69} + 253600 q^{71} + 19715 q^{73} + 165612 q^{75} + 28033 q^{77} + 10441 q^{79} - 32923 q^{81} + 20792 q^{83} + 105782 q^{85} - 156266 q^{87} + 49539 q^{89} + 240040 q^{91} - 72731 q^{93} + 263031 q^{95} + 213460 q^{97} - 530516 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(112, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.6.i.a $2$ $17.963$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-19$$ $$-19$$ $$140$$ $$q+(-19+19\zeta_{6})q^{3}-19\zeta_{6}q^{5}+(7+\cdots)q^{7}+\cdots$$
112.6.i.b $4$ $17.963$ $$\Q(\sqrt{-3}, \sqrt{130})$$ None $$0$$ $$-14$$ $$42$$ $$-232$$ $$q+(-7-\beta _{1}-7\beta _{2})q^{3}-21\beta _{2}q^{5}+\cdots$$
112.6.i.c $4$ $17.963$ $$\Q(\sqrt{-3}, \sqrt{37})$$ None $$0$$ $$-8$$ $$38$$ $$168$$ $$q+(-4\beta _{1}-\beta _{2})q^{3}+(19-19\beta _{1}-10\beta _{2}+\cdots)q^{5}+\cdots$$
112.6.i.d $4$ $17.963$ $$\Q(\sqrt{-3}, \sqrt{79})$$ None $$0$$ $$14$$ $$-70$$ $$0$$ $$q+(7+\beta _{1}+7\beta _{2})q^{3}+(-4\beta _{1}+35\beta _{2}+\cdots)q^{5}+\cdots$$
112.6.i.e $4$ $17.963$ $$\Q(\sqrt{-3}, \sqrt{109})$$ None $$0$$ $$28$$ $$-42$$ $$-112$$ $$q+(14-14\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-21\beta _{1}+\cdots)q^{5}+\cdots$$
112.6.i.f $10$ $17.963$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$5$$ $$81$$ $$-116$$ $$q+(1-\beta _{1}-\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+2^{4}\beta _{3}+\cdots)q^{5}+\cdots$$
112.6.i.g $10$ $17.963$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$13$$ $$-31$$ $$92$$ $$q+(3+3\beta _{1}+\beta _{4})q^{3}+(6\beta _{1}-\beta _{6})q^{5}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(112, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(112, [\chi]) \simeq$$ $$S_{6}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 2}$$