# Properties

 Label 66.2.h Level $66$ Weight $2$ Character orbit 66.h Rep. character $\chi_{66}(17,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $16$ Newform subspaces $2$ Sturm bound $24$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$66 = 2 \cdot 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 66.h (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(66, [\chi])$$.

Total New Old
Modular forms 64 16 48
Cusp forms 32 16 16
Eisenstein series 32 0 32

## Trace form

 $$16 q + 4 q^{3} - 4 q^{4} - 5 q^{6} - 16 q^{9} + O(q^{10})$$ $$16 q + 4 q^{3} - 4 q^{4} - 5 q^{6} - 16 q^{9} - 6 q^{12} - 12 q^{15} - 4 q^{16} - 5 q^{18} - 30 q^{19} + 12 q^{22} + 5 q^{24} - 12 q^{25} + 10 q^{27} + 10 q^{28} + 30 q^{30} + 26 q^{31} + 37 q^{33} + 20 q^{34} + 9 q^{36} + 12 q^{37} + 10 q^{39} + 10 q^{40} - 4 q^{42} - 16 q^{45} - 20 q^{46} + 4 q^{48} - 36 q^{49} - 15 q^{51} - 20 q^{52} - 28 q^{55} + 35 q^{57} - 46 q^{58} + 8 q^{60} - 20 q^{61} + 10 q^{63} - 4 q^{64} - 52 q^{66} - 4 q^{67} - 2 q^{69} - 34 q^{70} - 20 q^{72} + 10 q^{73} - 33 q^{75} - 16 q^{78} + 20 q^{79} - 12 q^{81} + 6 q^{82} + 60 q^{85} + 12 q^{88} + 10 q^{90} + 48 q^{91} - 26 q^{93} + 80 q^{94} + 18 q^{97} + 46 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(66, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
66.2.h.a $8$ $0.527$ 8.0.185640625.1 None $$-2$$ $$2$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$$
66.2.h.b $8$ $0.527$ 8.0.185640625.1 None $$2$$ $$2$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(66, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(66, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 2}$$