# Properties

 Label 930.2.j Level $930$ Weight $2$ Character orbit 930.j Rep. character $\chi_{930}(497,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $120$ Newform subspaces $8$ Sturm bound $384$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$8$$ Sturm bound: $$384$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(930, [\chi])$$.

Total New Old
Modular forms 400 120 280
Cusp forms 368 120 248
Eisenstein series 32 0 32

## Trace form

 $$120 q + 8 q^{6} + O(q^{10})$$ $$120 q + 8 q^{6} - 24 q^{15} - 120 q^{16} - 16 q^{18} - 16 q^{21} + 24 q^{27} + 40 q^{33} + 8 q^{36} + 16 q^{37} - 16 q^{40} - 32 q^{42} - 48 q^{43} + 56 q^{45} - 48 q^{46} + 32 q^{51} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 16 q^{60} + 80 q^{61} - 48 q^{63} - 48 q^{66} - 16 q^{67} - 32 q^{70} + 16 q^{72} + 80 q^{73} - 64 q^{75} + 16 q^{78} + 40 q^{81} + 32 q^{82} - 80 q^{85} + 40 q^{87} - 32 q^{90} - 8 q^{96} - 32 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(930, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
930.2.j.a $4$ $7.426$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\zeta_{8}^{3}q^{2}+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$$
930.2.j.b $4$ $7.426$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}-\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$$
930.2.j.c $8$ $7.426$ 8.0.1698758656.6 None $$0$$ $$-8$$ $$0$$ $$4$$ $$q-\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{7})q^{3}-\beta _{7}q^{4}+\cdots$$
930.2.j.d $8$ $7.426$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\zeta_{24}q^{2}+\zeta_{24}^{2}q^{3}+\zeta_{24}^{3}q^{4}+(\zeta_{24}+\cdots)q^{5}+\cdots$$
930.2.j.e $8$ $7.426$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+(\zeta_{24}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots$$
930.2.j.f $8$ $7.426$ 8.0.1698758656.6 None $$0$$ $$8$$ $$0$$ $$4$$ $$q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{7})q^{3}-\beta _{7}q^{4}+\cdots$$
930.2.j.g $40$ $7.426$ None $$0$$ $$-4$$ $$0$$ $$-8$$
930.2.j.h $40$ $7.426$ None $$0$$ $$-4$$ $$0$$ $$-8$$

## Decomposition of $$S_{2}^{\mathrm{old}}(930, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(930, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$