# Properties

 Label 666.2.be Level $666$ Weight $2$ Character orbit 666.be Rep. character $\chi_{666}(125,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $40$ Newform subspaces $4$ Sturm bound $228$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$666 = 2 \cdot 3^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 666.be (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$111$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$4$$ Sturm bound: $$228$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 488 40 448
Cusp forms 424 40 384
Eisenstein series 64 0 64

## Trace form

 $$40 q + O(q^{10})$$ $$40 q + 12 q^{13} + 20 q^{16} - 24 q^{19} + 16 q^{22} + 24 q^{28} + 8 q^{31} + 64 q^{37} + 12 q^{40} + 8 q^{43} + 16 q^{46} + 36 q^{49} - 12 q^{52} - 16 q^{55} - 12 q^{58} + 12 q^{61} - 96 q^{67} + 16 q^{70} + 24 q^{76} - 88 q^{79} - 20 q^{82} + 32 q^{88} - 88 q^{91} + 16 q^{94} + 4 q^{97} + O(q^{100})$$

## 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.be.a $8$ $5.318$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{5}+\cdots$$
666.2.be.b $8$ $5.318$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(2\zeta_{24}^{3}+2\zeta_{24}^{7})q^{5}+\cdots$$
666.2.be.c $8$ $5.318$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{5}+\cdots$$
666.2.be.d $16$ $5.318$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{10}q^{2}-\beta _{9}q^{4}+(\beta _{1}+\beta _{7})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots$$

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

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