# Properties

 Label 42.2.e Level $42$ Weight $2$ Character orbit 42.e Rep. character $\chi_{42}(25,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $4$ Newform subspaces $2$ Sturm bound $16$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$42 = 2 \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 42.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$16$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(42, [\chi])$$.

Total New Old
Modular forms 24 4 20
Cusp forms 8 4 4
Eisenstein series 16 0 16

## Trace form

 $$4 q - 2 q^{4} - 4 q^{5} - 4 q^{6} + 6 q^{7} - 2 q^{9} + O(q^{10})$$ $$4 q - 2 q^{4} - 4 q^{5} - 4 q^{6} + 6 q^{7} - 2 q^{9} + 2 q^{10} - 8 q^{11} - 8 q^{13} + 8 q^{14} + 4 q^{15} - 2 q^{16} + 4 q^{17} - 4 q^{19} + 8 q^{20} + 4 q^{21} + 4 q^{22} + 4 q^{23} + 2 q^{24} - 4 q^{26} - 6 q^{28} + 8 q^{29} + 4 q^{30} - 2 q^{31} + 2 q^{33} - 8 q^{34} - 8 q^{35} + 4 q^{36} - 4 q^{37} - 12 q^{38} + 4 q^{39} + 2 q^{40} - 6 q^{42} - 16 q^{43} - 8 q^{44} - 4 q^{45} + 4 q^{46} + 12 q^{47} - 2 q^{49} - 16 q^{50} - 4 q^{51} + 4 q^{52} + 12 q^{53} + 2 q^{54} + 28 q^{55} - 4 q^{56} - 24 q^{57} + 14 q^{58} + 8 q^{59} - 2 q^{60} + 16 q^{61} + 8 q^{62} + 4 q^{64} + 12 q^{65} + 8 q^{66} + 12 q^{67} + 4 q^{68} + 8 q^{69} - 2 q^{70} - 8 q^{71} - 12 q^{73} + 12 q^{74} - 8 q^{75} + 8 q^{76} - 28 q^{77} + 8 q^{78} - 2 q^{79} - 4 q^{80} - 2 q^{81} - 32 q^{83} - 8 q^{84} - 8 q^{85} - 12 q^{86} - 14 q^{87} - 2 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} + 4 q^{93} + 4 q^{95} + 2 q^{96} + 12 q^{97} + 24 q^{98} + 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(42, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
42.2.e.a $2$ $0.335$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$-1$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-1+\cdots)q^{5}+\cdots$$
42.2.e.b $2$ $0.335$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-3$$ $$5$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(42, [\chi])$$ into lower level spaces

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