# Properties

 Label 126.2.t Level $126$ Weight $2$ Character orbit 126.t Rep. character $\chi_{126}(47,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$126 = 2 \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 126.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(126, [\chi])$$.

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

## Trace form

 $$16q + 8q^{4} + 2q^{7} - 6q^{9} + O(q^{10})$$ $$16q + 8q^{4} + 2q^{7} - 6q^{9} - 6q^{13} - 6q^{14} - 18q^{15} - 8q^{16} + 18q^{17} + 12q^{18} - 18q^{21} - 6q^{24} + 16q^{25} - 12q^{26} - 36q^{27} - 2q^{28} + 6q^{29} - 18q^{30} + 6q^{31} + 18q^{33} - 30q^{35} - 2q^{37} - 30q^{39} + 6q^{41} + 30q^{42} - 2q^{43} + 12q^{44} + 12q^{45} + 6q^{46} - 18q^{47} + 10q^{49} - 12q^{50} + 36q^{53} + 18q^{54} + 6q^{57} - 12q^{58} + 30q^{59} - 6q^{60} - 60q^{61} - 36q^{62} + 42q^{63} - 16q^{64} + 42q^{65} + 48q^{66} + 14q^{67} + 36q^{68} + 42q^{69} + 30q^{75} - 18q^{77} - 16q^{79} + 54q^{81} - 18q^{84} - 12q^{85} - 48q^{87} + 24q^{89} - 18q^{90} - 12q^{91} + 6q^{92} + 30q^{93} - 66q^{95} - 6q^{96} - 6q^{97} + 24q^{98} + 18q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(126, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
126.2.t.a $$16$$ $$1.006$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+(-\beta _{1}+\beta _{6})q^{2}+(-\beta _{11}-\beta _{14})q^{3}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(126, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(126, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$