# Properties

 Label 114.2.l Level $114$ Weight $2$ Character orbit 114.l Rep. character $\chi_{114}(29,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $36$ Newform subspaces $2$ Sturm bound $40$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$114 = 2 \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 114.l (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$2$$ Sturm bound: $$40$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 144 36 108
Cusp forms 96 36 60
Eisenstein series 48 0 48

## Trace form

 $$36 q + 3 q^{3} + 3 q^{6} - 3 q^{9} + O(q^{10})$$ $$36 q + 3 q^{3} + 3 q^{6} - 3 q^{9} - 24 q^{13} - 6 q^{15} - 12 q^{19} - 48 q^{22} + 3 q^{24} - 36 q^{25} - 9 q^{27} + 12 q^{28} - 51 q^{33} - 12 q^{34} - 3 q^{36} + 12 q^{39} - 12 q^{43} + 36 q^{46} + 6 q^{48} + 42 q^{49} + 9 q^{51} - 12 q^{52} + 54 q^{54} + 60 q^{55} + 24 q^{57} + 24 q^{58} + 42 q^{60} + 108 q^{61} + 66 q^{63} - 18 q^{64} + 3 q^{66} - 30 q^{67} + 54 q^{69} + 48 q^{70} + 6 q^{72} - 84 q^{73} - 42 q^{78} - 12 q^{79} - 3 q^{81} + 6 q^{82} - 54 q^{84} - 54 q^{87} - 12 q^{90} - 36 q^{91} - 150 q^{93} + 18 q^{97} - 132 q^{99} + O(q^{100})$$

## 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.l.a $18$ $0.910$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{6}-\beta _{7})q^{2}+(\beta _{1}-\beta _{17})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots$$
114.2.l.b $18$ $0.910$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+\beta _{5}q^{3}-\beta _{7}q^{4}+(\beta _{9}-\beta _{17})q^{5}+\cdots$$

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

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