Properties

 Label 2160.2.f Level $2160$ Weight $2$ Character orbit 2160.f Rep. character $\chi_{2160}(1729,\cdot)$ Character field $\Q$ Dimension $48$ Newform subspaces $15$ Sturm bound $864$ Trace bound $19$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$2160 = 2^{4} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2160.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$15$$ Sturm bound: $$864$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2160, [\chi])$$.

Total New Old
Modular forms 468 48 420
Cusp forms 396 48 348
Eisenstein series 72 0 72

Trace form

 $$48 q + O(q^{10})$$ $$48 q - 4 q^{19} - 4 q^{25} + 4 q^{31} - 40 q^{49} - 20 q^{55} + 24 q^{61} + 20 q^{79} - 24 q^{85} - 24 q^{91} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(2160, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2160.2.f.a $2$ $17.248$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2+i)q^{5}+2iq^{7}-2q^{11}-6iq^{13}+\cdots$$
2160.2.f.b $2$ $17.248$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2-i)q^{5}+2iq^{7}+2q^{11}-2iq^{13}+\cdots$$
2160.2.f.c $2$ $17.248$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+2i)q^{5}+4iq^{7}+q^{11}-iq^{13}+\cdots$$
2160.2.f.d $2$ $17.248$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-2i)q^{5}+4iq^{7}+5q^{11}-3iq^{13}+\cdots$$
2160.2.f.e $2$ $17.248$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+2i)q^{5}+4iq^{7}-5q^{11}-3iq^{13}+\cdots$$
2160.2.f.f $2$ $17.248$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1-2i)q^{5}+4iq^{7}-q^{11}-iq^{13}+\cdots$$
2160.2.f.g $2$ $17.248$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}+2iq^{7}-2q^{11}-2iq^{13}+\cdots$$
2160.2.f.h $2$ $17.248$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2-i)q^{5}+2iq^{7}+2q^{11}-6iq^{13}+\cdots$$
2160.2.f.i $4$ $17.248$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-1-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(-2+\cdots)q^{11}+\cdots$$
2160.2.f.j $4$ $17.248$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{5}+(-\beta _{1}-2\beta _{2})q^{17}+(-2+\cdots)q^{19}+\cdots$$
2160.2.f.k $4$ $17.248$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{3}q^{5}+\zeta_{8}q^{7}+(-\zeta_{8}^{2}+2\zeta_{8}^{3})q^{11}+\cdots$$
2160.2.f.l $4$ $17.248$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}+\beta _{2}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\cdots$$
2160.2.f.m $4$ $17.248$ $$\Q(i, \sqrt{19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{5}+(-1-2\beta _{3})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots$$
2160.2.f.n $4$ $17.248$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(1+\beta _{2}+\beta _{3})q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\cdots)q^{11}+\cdots$$
2160.2.f.o $8$ $17.248$ 8.0.2702336256.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{5}-\beta _{1}q^{7}+(-2\beta _{3}-\beta _{6}+2\beta _{7})q^{11}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(2160, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2160, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(270, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(360, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(540, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(720, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1080, [\chi])$$$$^{\oplus 2}$$