# Properties

 Label 112.2.w Level $112$ Weight $2$ Character orbit 112.w Rep. character $\chi_{112}(37,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $56$ Newform subspaces $3$ Sturm bound $32$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$112 = 2^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 112.w (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$112$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$3$$ Sturm bound: $$32$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 72 72 0
Cusp forms 56 56 0
Eisenstein series 16 16 0

## Trace form

 $$56 q - 2 q^{2} - 2 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} - 20 q^{8} + O(q^{10})$$ $$56 q - 2 q^{2} - 2 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} - 20 q^{8} + 4 q^{10} - 6 q^{11} - 2 q^{12} - 8 q^{13} - 24 q^{14} - 16 q^{15} + 8 q^{16} - 4 q^{17} + 10 q^{18} - 2 q^{19} + 8 q^{20} - 10 q^{21} - 36 q^{22} + 18 q^{24} - 2 q^{26} - 20 q^{27} - 14 q^{28} + 8 q^{29} + 14 q^{30} + 20 q^{31} + 8 q^{32} - 4 q^{33} - 32 q^{34} - 2 q^{35} - 64 q^{36} - 10 q^{37} + 18 q^{38} + 50 q^{40} + 30 q^{42} - 16 q^{43} - 14 q^{44} - 28 q^{45} - 44 q^{47} + 40 q^{48} - 8 q^{49} + 24 q^{50} + 30 q^{51} + 4 q^{52} + 6 q^{53} + 82 q^{54} + 72 q^{56} - 14 q^{58} - 18 q^{59} + 22 q^{60} - 2 q^{61} + 28 q^{62} - 36 q^{63} + 80 q^{64} - 4 q^{65} + 2 q^{66} + 30 q^{67} + 24 q^{68} - 20 q^{69} + 76 q^{70} - 24 q^{72} - 38 q^{74} - 24 q^{75} - 68 q^{76} - 18 q^{77} + 132 q^{78} - 4 q^{79} - 52 q^{80} - 8 q^{81} - 18 q^{82} + 32 q^{83} + 68 q^{84} + 12 q^{85} - 44 q^{86} - 34 q^{88} - 20 q^{90} + 32 q^{91} + 68 q^{92} + 10 q^{93} - 54 q^{94} + 20 q^{95} - 128 q^{96} - 16 q^{97} - 28 q^{98} + 8 q^{99} + O(q^{100})$$

## 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.w.a $4$ $0.894$ $$\Q(\zeta_{12})$$ None $$-2$$ $$-4$$ $$-6$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots$$
112.2.w.b $4$ $0.894$ $$\Q(\zeta_{12})$$ None $$4$$ $$2$$ $$0$$ $$0$$ $$q+(1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$$
112.2.w.c $48$ $0.894$ None $$-4$$ $$0$$ $$4$$ $$0$$