# Properties

 Label 114.2.h Level $114$ Weight $2$ Character orbit 114.h Rep. character $\chi_{114}(65,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $6$ Sturm bound $40$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$114 = 2 \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 114.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$40$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(114, [\chi])$$.

Total New Old
Modular forms 48 16 32
Cusp forms 32 16 16
Eisenstein series 16 0 16

## Trace form

 $$16 q - 3 q^{3} - 8 q^{4} - q^{6} + 12 q^{7} + q^{9} + O(q^{10})$$ $$16 q - 3 q^{3} - 8 q^{4} - q^{6} + 12 q^{7} + q^{9} - 18 q^{13} + 6 q^{15} - 8 q^{16} - 18 q^{19} - 6 q^{22} - q^{24} + 16 q^{25} - 6 q^{28} + 4 q^{30} - 3 q^{33} + 12 q^{34} + q^{36} - 48 q^{39} + 22 q^{42} + 2 q^{43} - 52 q^{45} + 3 q^{48} - 12 q^{49} + 72 q^{51} + 18 q^{52} + 20 q^{54} - 4 q^{55} + 48 q^{57} - 6 q^{60} - 18 q^{61} - 16 q^{63} + 16 q^{64} + 25 q^{66} + 36 q^{67} - 12 q^{70} + 3 q^{72} + 8 q^{73} + 12 q^{76} + 6 q^{78} - 30 q^{79} - 23 q^{81} - 6 q^{82} + 8 q^{85} - 12 q^{87} - 78 q^{90} - 6 q^{91} - 6 q^{93} + 2 q^{96} + 18 q^{97} + 23 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(114, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
114.2.h.a $2$ $0.910$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$-6$$ $$-4$$ $$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
114.2.h.b $2$ $0.910$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$6$$ $$2$$ $$q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
114.2.h.c $2$ $0.910$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-3$$ $$-6$$ $$2$$ $$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
114.2.h.d $2$ $0.910$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$6$$ $$-4$$ $$q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
114.2.h.e $4$ $0.910$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$-2$$ $$4$$ $$0$$ $$8$$ $$q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$$
114.2.h.f $4$ $0.910$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$2$$ $$2$$ $$0$$ $$8$$ $$q+(1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(114, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(114, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 2}$$