Properties

 Label 4800.2.f Level $4800$ Weight $2$ Character orbit 4800.f Rep. character $\chi_{4800}(3649,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $36$ Sturm bound $1920$ Trace bound $31$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$4800 = 2^{6} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4800.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$36$$ Sturm bound: $$1920$$ Trace bound: $$31$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$, $$19$$, $$23$$, $$31$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4800, [\chi])$$.

Total New Old
Modular forms 1032 72 960
Cusp forms 888 72 816
Eisenstein series 144 0 144

Trace form

 $$72 q - 72 q^{9} + O(q^{10})$$ $$72 q - 72 q^{9} - 16 q^{41} - 72 q^{49} + 32 q^{61} - 32 q^{69} + 72 q^{81} - 16 q^{89} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(4800, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4800.2.f.a $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+5iq^{7}-q^{9}-6q^{11}-3iq^{13}+\cdots$$
4800.2.f.b $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{7}-q^{9}-6q^{11}-5iq^{13}+\cdots$$
4800.2.f.c $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}-4q^{11}+2iq^{13}-2iq^{17}+\cdots$$
4800.2.f.d $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}-4q^{11}+2iq^{13}-2iq^{17}+\cdots$$
4800.2.f.e $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}-4q^{11}+2iq^{13}+\cdots$$
4800.2.f.f $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{7}-q^{9}-4q^{11}+7iq^{13}+\cdots$$
4800.2.f.g $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}-4q^{11}+3iq^{13}+\cdots$$
4800.2.f.h $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}-4q^{11}-6iq^{13}+\cdots$$
4800.2.f.i $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}-4q^{11}+6iq^{13}-6iq^{17}+\cdots$$
4800.2.f.j $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}-4q^{11}-2iq^{13}+2iq^{17}+\cdots$$
4800.2.f.k $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}-2q^{11}-3iq^{13}+\cdots$$
4800.2.f.l $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}-2q^{11}-iq^{13}+\cdots$$
4800.2.f.m $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{7}-q^{9}-5iq^{13}-5q^{19}+\cdots$$
4800.2.f.n $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}+6iq^{13}+2iq^{17}+\cdots$$
4800.2.f.o $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}-2iq^{13}-6iq^{17}-4q^{19}+\cdots$$
4800.2.f.p $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}-2iq^{13}-6iq^{17}+\cdots$$
4800.2.f.q $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}-iq^{13}-3q^{19}+\cdots$$
4800.2.f.r $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}+2iq^{13}+6iq^{17}+\cdots$$
4800.2.f.s $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}-2iq^{13}-6iq^{17}+\cdots$$
4800.2.f.t $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}+iq^{13}+3q^{19}+\cdots$$
4800.2.f.u $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}-6iq^{13}-2iq^{17}+\cdots$$
4800.2.f.v $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}+2iq^{13}+6iq^{17}+4q^{19}+\cdots$$
4800.2.f.w $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}+2iq^{13}+6iq^{17}+\cdots$$
4800.2.f.x $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{7}-q^{9}+5iq^{13}+5q^{19}+\cdots$$
4800.2.f.y $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}+2q^{11}+iq^{13}+\cdots$$
4800.2.f.z $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}+2q^{11}+3iq^{13}+\cdots$$
4800.2.f.ba $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}+4q^{11}+2iq^{13}-2iq^{17}+\cdots$$
4800.2.f.bb $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}+4q^{11}+6iq^{13}+\cdots$$
4800.2.f.bc $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}+4q^{11}-6iq^{13}+6iq^{17}+\cdots$$
4800.2.f.bd $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}+4q^{11}-3iq^{13}+\cdots$$
4800.2.f.be $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{7}-q^{9}+4q^{11}-7iq^{13}+\cdots$$
4800.2.f.bf $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}+4q^{11}+2iq^{13}-2iq^{17}+\cdots$$
4800.2.f.bg $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}+4q^{11}+2iq^{13}-2iq^{17}+\cdots$$
4800.2.f.bh $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}+4q^{11}-2iq^{13}+\cdots$$
4800.2.f.bi $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{7}-q^{9}+6q^{11}+5iq^{13}+\cdots$$
4800.2.f.bj $2$ $38.328$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+5iq^{7}-q^{9}+6q^{11}+3iq^{13}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(4800, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4800, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(200, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(400, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(600, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(800, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(960, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1200, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1600, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2400, [\chi])$$$$^{\oplus 2}$$