# Properties

 Label 3120.2.l Level $3120$ Weight $2$ Character orbit 3120.l Rep. character $\chi_{3120}(1249,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $17$ Sturm bound $1344$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3120.l (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$17$$ Sturm bound: $$1344$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3120, [\chi])$$.

Total New Old
Modular forms 696 72 624
Cusp forms 648 72 576
Eisenstein series 48 0 48

## Trace form

 $$72 q - 72 q^{9} + O(q^{10})$$ $$72 q - 72 q^{9} - 32 q^{19} - 8 q^{25} - 16 q^{31} + 48 q^{35} + 8 q^{39} - 56 q^{49} + 8 q^{51} + 16 q^{55} - 16 q^{61} + 16 q^{69} - 8 q^{75} - 8 q^{79} + 72 q^{81} - 16 q^{85} + 24 q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3120, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3120.2.l.a $2$ $24.913$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-iq^{3}+(-2-i)q^{5}-q^{9}+6q^{11}+\cdots$$
3120.2.l.b $2$ $24.913$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1-2i)q^{5}+5iq^{7}-q^{9}+\cdots$$
3120.2.l.c $2$ $24.913$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1-2i)q^{5}+iq^{7}-q^{9}+\cdots$$
3120.2.l.d $2$ $24.913$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1+2i)q^{5}+iq^{7}-q^{9}+\cdots$$
3120.2.l.e $2$ $24.913$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-iq^{3}+(1-2i)q^{5}+iq^{7}-q^{9}-3q^{11}+\cdots$$
3120.2.l.f $2$ $24.913$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-2i)q^{5}+3iq^{7}-q^{9}+\cdots$$
3120.2.l.g $2$ $24.913$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q-iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}-2q^{11}+\cdots$$
3120.2.l.h $2$ $24.913$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{3}+(2+i)q^{5}+4iq^{7}-q^{9}-2q^{11}+\cdots$$
3120.2.l.i $2$ $24.913$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{3}+(2-i)q^{5}+4iq^{7}-q^{9}+6q^{11}+\cdots$$
3120.2.l.j $4$ $24.913$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{2}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}-2\beta _{2}q^{7}+\cdots$$
3120.2.l.k $4$ $24.913$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$$
3120.2.l.l $4$ $24.913$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(2\zeta_{8}+\cdots)q^{7}+\cdots$$
3120.2.l.m $6$ $24.913$ 6.0.5161984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}-\beta _{5}q^{5}-q^{9}+(2-\beta _{4}-\beta _{5})q^{11}+\cdots$$
3120.2.l.n $8$ $24.913$ 8.0.$$\cdots$$.2 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{2}q^{3}-\beta _{6}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots$$
3120.2.l.o $8$ $24.913$ 8.0.1698758656.6 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+\beta _{4}q^{7}+\cdots$$
3120.2.l.p $10$ $24.913$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{5}q^{5}+(-\beta _{2}-\beta _{9})q^{7}+\cdots$$
3120.2.l.q $10$ $24.913$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{3}q^{5}-\beta _{9}q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(3120, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3120, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(260, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(390, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(520, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(780, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1040, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1560, [\chi])$$$$^{\oplus 2}$$