# Properties

 Label 84.12.k Level $84$ Weight $12$ Character orbit 84.k Rep. character $\chi_{84}(5,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $58$ Newform subspaces $2$ Sturm bound $192$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$84 = 2^{2} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$12$$ Character orbit: $$[\chi]$$ $$=$$ 84.k (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$192$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{12}(84, [\chi])$$.

Total New Old
Modular forms 364 58 306
Cusp forms 340 58 282
Eisenstein series 24 0 24

## Trace form

 $$58 q + 49691 q^{7} + 4800 q^{9} + O(q^{10})$$ $$58 q + 49691 q^{7} + 4800 q^{9} - 4853058 q^{15} + 17429355 q^{19} + 26105805 q^{21} - 267773069 q^{25} - 822204681 q^{31} + 40874949 q^{33} + 31938895 q^{37} + 565755201 q^{39} - 2617228910 q^{43} + 4109921793 q^{45} + 1214067217 q^{49} - 694793715 q^{51} + 9127314180 q^{57} + 51061188606 q^{61} + 6356584680 q^{63} + 180387533 q^{67} - 19258404003 q^{73} - 125519454729 q^{75} + 106477938065 q^{79} + 13567222728 q^{81} + 4658488716 q^{85} + 243101263104 q^{87} - 20346170205 q^{91} - 123898766976 q^{93} + 157345775874 q^{99} + O(q^{100})$$

## Decomposition of $$S_{12}^{\mathrm{new}}(84, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
84.12.k.a $2$ $64.541$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$729$$ $$0$$ $$76885$$ $$q+(3^{5}+3^{5}\zeta_{6})q^{3}+(51346-25807\zeta_{6})q^{7}+\cdots$$
84.12.k.b $56$ $64.541$ None $$0$$ $$-729$$ $$0$$ $$-27194$$

## Decomposition of $$S_{12}^{\mathrm{old}}(84, [\chi])$$ into lower level spaces

$$S_{12}^{\mathrm{old}}(84, [\chi]) \cong$$ $$S_{12}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{12}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$