# Properties

 Label 98.2.c Level $98$ Weight $2$ Character orbit 98.c Rep. character $\chi_{98}(67,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $8$ Newform subspaces $3$ Sturm bound $28$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$98 = 2 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 98.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ Sturm bound: $$28$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(98, [\chi])$$.

Total New Old
Modular forms 44 8 36
Cusp forms 12 8 4
Eisenstein series 32 0 32

## Trace form

 $$8 q - 4 q^{4} + O(q^{10})$$ $$8 q - 4 q^{4} + 4 q^{11} - 16 q^{15} - 4 q^{16} + 4 q^{18} - 8 q^{22} + 8 q^{23} + 4 q^{25} - 16 q^{29} + 8 q^{30} - 24 q^{37} - 16 q^{39} + 40 q^{43} + 4 q^{44} + 8 q^{46} + 32 q^{50} + 20 q^{51} - 8 q^{53} + 24 q^{57} - 16 q^{58} + 8 q^{60} + 8 q^{64} - 16 q^{67} - 48 q^{71} + 4 q^{72} - 16 q^{74} - 32 q^{78} - 8 q^{79} + 32 q^{81} - 16 q^{85} + 12 q^{86} + 4 q^{88} - 16 q^{92} + 8 q^{93} + 40 q^{95} + 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(98, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
98.2.c.a $2$ $0.783$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-2$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
98.2.c.b $2$ $0.783$ $$\Q(\sqrt{-3})$$ None $$1$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
98.2.c.c $4$ $0.783$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(98, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(98, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 2}$$