# Properties

 Label 112.7.s Level $112$ Weight $7$ Character orbit 112.s Rep. character $\chi_{112}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $46$ Newform subspaces $5$ Sturm bound $112$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$112 = 2^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 112.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$112$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(112, [\chi])$$.

Total New Old
Modular forms 204 50 154
Cusp forms 180 46 134
Eisenstein series 24 4 20

## Trace form

 $$46 q + 3 q^{3} - 3 q^{5} - 358 q^{7} + 5102 q^{9} + O(q^{10})$$ $$46 q + 3 q^{3} - 3 q^{5} - 358 q^{7} + 5102 q^{9} + 681 q^{11} + 1462 q^{15} - 3 q^{17} + 15123 q^{19} - 8755 q^{21} + 12185 q^{23} + 47446 q^{25} - 16068 q^{29} - 110877 q^{31} - 13611 q^{33} + 89187 q^{35} - 1801 q^{37} + 42736 q^{39} + 102004 q^{43} + 228810 q^{45} + 188499 q^{47} - 113666 q^{49} - 301413 q^{51} + 50159 q^{53} + 417850 q^{57} + 664611 q^{59} + 264597 q^{61} + 798434 q^{63} + 103952 q^{65} - 360767 q^{67} - 808028 q^{71} - 385563 q^{73} + 811950 q^{75} - 770393 q^{77} + 572089 q^{79} - 955143 q^{81} + 619338 q^{85} - 3755130 q^{87} - 881499 q^{89} - 3439920 q^{91} + 563149 q^{93} + 2991867 q^{95} + 714148 q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(112, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.7.s.a $2$ $25.766$ $$\Q(\sqrt{-3})$$ None $$0$$ $$21$$ $$315$$ $$686$$ $$q+(7+7\zeta_{6})q^{3}+(210-105\zeta_{6})q^{5}+\cdots$$
112.7.s.b $4$ $25.766$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-18$$ $$-150$$ $$-280$$ $$q+(-6-3\beta _{1}-13\beta _{3})q^{3}+(-5^{2}+5^{2}\beta _{1}+\cdots)q^{5}+\cdots$$
112.7.s.c $8$ $25.766$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$-336$$ $$-652$$ $$q+(\beta _{3}+\beta _{7})q^{3}+(-56+28\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
112.7.s.d $8$ $25.766$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$168$$ $$452$$ $$q-\beta _{3}q^{3}+(28-14\beta _{1}-\beta _{5})q^{5}+(11^{2}+\cdots)q^{7}+\cdots$$
112.7.s.e $24$ $25.766$ None $$0$$ $$0$$ $$0$$ $$-564$$

## Decomposition of $$S_{7}^{\mathrm{old}}(112, [\chi])$$ into lower level spaces

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