# Properties

 Label 1560.2.l Level $1560$ Weight $2$ Character orbit 1560.l Rep. character $\chi_{1560}(1249,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $6$ Sturm bound $672$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1560.l (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$672$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1560, [\chi])$$.

Total New Old
Modular forms 352 36 316
Cusp forms 320 36 284
Eisenstein series 32 0 32

## Trace form

 $$36 q - 36 q^{9} + O(q^{10})$$ $$36 q - 36 q^{9} - 4 q^{15} + 24 q^{19} + 8 q^{21} - 20 q^{25} + 8 q^{31} - 8 q^{35} - 12 q^{49} - 40 q^{55} - 32 q^{59} + 16 q^{71} + 8 q^{79} + 36 q^{81} - 8 q^{85} + 16 q^{89} - 24 q^{91} + 8 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1560, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1560.2.l.a $2$ $12.457$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1+2i)q^{5}+5iq^{7}-q^{9}+\cdots$$
1560.2.l.b $2$ $12.457$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-iq^{3}+(1+2i)q^{5}+iq^{7}-q^{9}+3q^{11}+\cdots$$
1560.2.l.c $6$ $12.457$ 6.0.5161984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}-\beta _{5}q^{5}-q^{9}+(-2+\beta _{4}+\cdots)q^{11}+\cdots$$
1560.2.l.d $8$ $12.457$ 8.0.$$\cdots$$.2 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{2}q^{3}-\beta _{7}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots$$
1560.2.l.e $8$ $12.457$ 8.0.1698758656.6 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}-\beta _{4}q^{7}+\cdots$$
1560.2.l.f $10$ $12.457$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{2}q^{5}-\beta _{9}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1560, [\chi])$$ into lower level spaces

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