# Properties

 Label 84.2.b Level $84$ Weight $2$ Character orbit 84.b Rep. character $\chi_{84}(55,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $32$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$84 = 2^{2} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 84.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$32$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(84, [\chi])$$.

Total New Old
Modular forms 20 8 12
Cusp forms 12 8 4
Eisenstein series 8 0 8

## Trace form

 $$8q - 2q^{2} + 2q^{4} - 14q^{8} + 8q^{9} + O(q^{10})$$ $$8q - 2q^{2} + 2q^{4} - 14q^{8} + 8q^{9} - 2q^{14} - 14q^{16} - 2q^{18} - 4q^{21} + 12q^{22} - 16q^{25} + 18q^{28} - 16q^{29} + 16q^{30} + 18q^{32} + 2q^{36} - 24q^{37} - 16q^{42} + 28q^{44} - 12q^{46} + 16q^{49} + 38q^{50} + 32q^{53} - 22q^{56} - 24q^{57} + 4q^{58} - 8q^{60} + 2q^{64} + 16q^{65} - 8q^{70} - 14q^{72} - 28q^{74} - 16q^{77} - 24q^{78} + 8q^{81} + 16q^{84} + 40q^{85} - 60q^{86} - 4q^{88} - 28q^{92} + 30q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(84, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
84.2.b.a $$4$$ $$0.671$$ 4.0.2312.1 None $$-1$$ $$-4$$ $$0$$ $$2$$ $$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$$
84.2.b.b $$4$$ $$0.671$$ 4.0.2312.1 None $$-1$$ $$4$$ $$0$$ $$-2$$ $$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(84, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(84, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 2}$$