Properties

 Label 3332.1.m Level $3332$ Weight $1$ Character orbit 3332.m Rep. character $\chi_{3332}(2843,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $6$ Newform subspaces $3$ Sturm bound $504$ Trace bound $10$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$3332 = 2^{2} \cdot 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3332.m (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$68$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$504$$ Trace bound: $$10$$

Dimensions

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

Total New Old
Modular forms 44 26 18
Cusp forms 12 6 6
Eisenstein series 32 20 12

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

Trace form

 $$6 q - 6 q^{4} + 2 q^{5} + O(q^{10})$$ $$6 q - 6 q^{4} + 2 q^{5} - 2 q^{10} + 6 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 2 q^{29} + 2 q^{37} + 2 q^{40} - 2 q^{41} - 2 q^{45} + 2 q^{50} - 6 q^{58} + 2 q^{61} - 6 q^{64} - 8 q^{65} - 2 q^{68} - 2 q^{72} - 2 q^{73} + 6 q^{74} + 2 q^{80} - 6 q^{81} - 2 q^{82} - 2 q^{85} - 2 q^{90} + 2 q^{97} + O(q^{100})$$

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.m.a $2$ $1.663$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-iq^{2}-q^{4}+(-1-i)q^{5}+iq^{8}+\cdots$$
3332.1.m.b $2$ $1.663$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{2}-q^{4}+(1+i)q^{5}-iq^{8}+iq^{9}+\cdots$$
3332.1.m.c $2$ $1.663$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-iq^{2}-q^{4}+(1+i)q^{5}+iq^{8}+iq^{9}+\cdots$$

Decomposition of $$S_{1}^{\mathrm{old}}(3332, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(3332, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 3}$$