# Properties

 Label 42.2.d Level $42$ Weight $2$ Character orbit 42.d Rep. character $\chi_{42}(41,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $16$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$42 = 2 \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 42.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$16$$ Trace bound: $$0$$

## Dimensions

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

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

## Trace form

 $$4q - 4q^{4} - 4q^{7} + O(q^{10})$$ $$4q - 4q^{4} - 4q^{7} - 12q^{15} + 4q^{16} + 12q^{18} + 12q^{21} + 4q^{25} + 4q^{28} - 12q^{30} - 8q^{37} - 12q^{39} - 12q^{42} + 16q^{43} - 24q^{46} - 20q^{49} + 24q^{51} + 12q^{57} + 24q^{58} + 12q^{60} - 4q^{64} + 32q^{67} + 24q^{70} - 12q^{72} + 12q^{78} - 40q^{79} - 36q^{81} - 12q^{84} - 48q^{85} + 24q^{91} + O(q^{100})$$

## 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.d.a $$4$$ $$0.335$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$$