# Properties

 Label 190.2.i Level $190$ Weight $2$ Character orbit 190.i Rep. character $\chi_{190}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $20$ Newform subspaces $1$ Sturm bound $60$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$190 = 2 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 190.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$60$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 68 20 48
Cusp forms 52 20 32
Eisenstein series 16 0 16

## Trace form

 $$20 q + 10 q^{4} - 2 q^{5} + 10 q^{9} + O(q^{10})$$ $$20 q + 10 q^{4} - 2 q^{5} + 10 q^{9} - 12 q^{11} - 10 q^{14} - 2 q^{15} - 10 q^{16} - 22 q^{19} - 4 q^{20} + 40 q^{21} - 6 q^{25} + 8 q^{26} - 4 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} - 2 q^{35} - 10 q^{36} - 32 q^{39} + 2 q^{41} - 6 q^{44} - 56 q^{45} - 52 q^{46} + 40 q^{49} + 40 q^{50} + 8 q^{51} + 36 q^{54} + 18 q^{55} - 20 q^{56} - 44 q^{59} + 2 q^{60} - 4 q^{61} - 20 q^{64} + 48 q^{65} + 4 q^{66} + 48 q^{69} - 8 q^{70} - 44 q^{71} + 10 q^{74} - 56 q^{75} + 4 q^{76} - 4 q^{79} - 2 q^{80} - 10 q^{81} + 80 q^{84} + 12 q^{85} + 2 q^{89} + 42 q^{90} + 20 q^{91} - 40 q^{94} - 4 q^{95} - 26 q^{99} + O(q^{100})$$

## 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.i.a $20$ $1.517$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\beta _{2}-\beta _{13})q^{2}-\beta _{1}q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$$

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

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