# Properties

 Label 190.2.k Level $190$ Weight $2$ Character orbit 190.k Rep. character $\chi_{190}(61,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $48$ Newform subspaces $4$ Sturm bound $60$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$190 = 2 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 190.k (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$4$$ Sturm bound: $$60$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(190, [\chi])$$.

Total New Old
Modular forms 204 48 156
Cusp forms 156 48 108
Eisenstein series 48 0 48

## Trace form

 $$48 q + 6 q^{3} + 6 q^{6} + 6 q^{8} + 6 q^{9} + O(q^{10})$$ $$48 q + 6 q^{3} + 6 q^{6} + 6 q^{8} + 6 q^{9} - 24 q^{13} - 12 q^{14} - 12 q^{17} - 36 q^{18} + 12 q^{19} - 24 q^{22} - 24 q^{23} + 6 q^{24} - 6 q^{26} - 6 q^{27} + 12 q^{28} + 12 q^{29} - 12 q^{31} + 42 q^{33} + 24 q^{34} + 6 q^{35} + 6 q^{36} + 24 q^{37} + 18 q^{38} - 24 q^{39} - 12 q^{41} + 24 q^{42} + 36 q^{43} - 6 q^{44} - 84 q^{47} - 12 q^{48} - 60 q^{49} + 6 q^{50} + 18 q^{51} + 12 q^{52} - 84 q^{53} - 54 q^{54} + 24 q^{56} - 84 q^{57} - 48 q^{58} - 78 q^{59} + 60 q^{61} - 60 q^{62} - 60 q^{63} - 24 q^{64} + 18 q^{65} + 30 q^{66} + 18 q^{67} - 6 q^{68} - 36 q^{69} + 36 q^{71} - 12 q^{72} + 24 q^{73} + 18 q^{74} + 6 q^{76} + 72 q^{77} + 36 q^{78} + 72 q^{79} - 6 q^{81} + 42 q^{82} + 36 q^{83} + 84 q^{87} + 12 q^{88} + 84 q^{89} + 24 q^{90} + 12 q^{91} + 12 q^{92} + 72 q^{93} + 60 q^{94} + 18 q^{97} + 24 q^{98} + 144 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(190, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
190.2.k.a $6$ $1.517$ $$\Q(\zeta_{18})$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots$$
190.2.k.b $12$ $1.517$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$6$$ $$q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$$
190.2.k.c $12$ $1.517$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$3$$ $$0$$ $$-6$$ $$q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots$$
190.2.k.d $18$ $1.517$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(190, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(190, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 2}$$