# Properties

 Label 666.2.bs Level $666$ Weight $2$ Character orbit 666.bs Rep. character $\chi_{666}(17,\cdot)$ Character field $\Q(\zeta_{36})$ Dimension $168$ Newform subspaces $2$ Sturm bound $228$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$666 = 2 \cdot 3^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 666.bs (of order $$36$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$111$$ Character field: $$\Q(\zeta_{36})$$ Newform subspaces: $$2$$ Sturm bound: $$228$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(666, [\chi])$$.

Total New Old
Modular forms 1464 168 1296
Cusp forms 1272 168 1104
Eisenstein series 192 0 192

## Trace form

 $$168 q + O(q^{10})$$ $$168 q + 48 q^{31} + 144 q^{34} + 96 q^{37} + 24 q^{40} + 96 q^{43} + 96 q^{46} - 48 q^{49} + 12 q^{58} + 96 q^{67} - 48 q^{70} + 48 q^{79} + 48 q^{82} - 48 q^{88} + 48 q^{91} - 144 q^{94} - 240 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(666, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
666.2.bs.a $72$ $5.318$ None $$0$$ $$0$$ $$0$$ $$0$$
666.2.bs.b $96$ $5.318$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(666, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(666, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(111, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(222, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(333, [\chi])$$$$^{\oplus 2}$$