Properties

 Label 3332.1.cc Level $3332$ Weight $1$ Character orbit 3332.cc Rep. character $\chi_{3332}(135,\cdot)$ Character field $\Q(\zeta_{42})$ Dimension $48$ Newform subspaces $3$ Sturm bound $504$ Trace bound $3$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$3332 = 2^{2} \cdot 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3332.cc (of order $$42$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3332$$ Character field: $$\Q(\zeta_{42})$$ Newform subspaces: $$3$$ Sturm bound: $$504$$ Trace bound: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3332, [\chi])$$.

Total New Old
Modular forms 96 96 0
Cusp forms 48 48 0
Eisenstein series 48 48 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 48 0 0 0

Trace form

 $$48 q + 4 q^{4} + 4 q^{9} + O(q^{10})$$ $$48 q + 4 q^{4} + 4 q^{9} + 4 q^{16} + 4 q^{17} - 4 q^{18} + 4 q^{21} + 4 q^{25} - 4 q^{26} - 4 q^{33} - 8 q^{36} + 4 q^{42} - 4 q^{53} - 8 q^{64} + 8 q^{66} - 24 q^{68} - 20 q^{69} - 4 q^{72} - 8 q^{77} + 56 q^{81} - 8 q^{84} - 4 q^{93} - 24 q^{98} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(3332, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3332.1.cc.a $12$ $1.663$ $$\Q(\zeta_{21})$$ $D_{21}$ $$\Q(\sqrt{-17})$$ None $$1$$ $$-13$$ $$0$$ $$2$$ $$q-\zeta_{42}^{17}q^{2}+(-1+\zeta_{42}^{11})q^{3}-\zeta_{42}^{13}q^{4}+\cdots$$
3332.1.cc.b $12$ $1.663$ $$\Q(\zeta_{21})$$ $D_{21}$ $$\Q(\sqrt{-17})$$ None $$1$$ $$13$$ $$0$$ $$-2$$ $$q-\zeta_{42}^{17}q^{2}+(1-\zeta_{42}^{11})q^{3}-\zeta_{42}^{13}q^{4}+\cdots$$
3332.1.cc.c $24$ $1.663$ $$\Q(\zeta_{84})$$ $D_{42}$ $$\Q(\sqrt{-17})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{84}^{40}q^{2}+(\zeta_{84}^{21}-\zeta_{84}^{37})q^{3}+\cdots$$