# Properties

 Label 5376.2.c Level $5376$ Weight $2$ Character orbit 5376.c Rep. character $\chi_{5376}(2689,\cdot)$ Character field $\Q$ Dimension $96$ Newform subspaces $40$ Sturm bound $2048$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5376 = 2^{8} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5376.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$40$$ Sturm bound: $$2048$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$, $$17$$, $$23$$, $$31$$, $$47$$, $$71$$, $$79$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(5376, [\chi])$$.

Total New Old
Modular forms 1072 96 976
Cusp forms 976 96 880
Eisenstein series 96 0 96

## Trace form

 $$96 q - 96 q^{9} + O(q^{10})$$ $$96 q - 96 q^{9} - 96 q^{25} + 96 q^{49} + 64 q^{65} - 64 q^{73} + 96 q^{81} - 64 q^{89} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(5376, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5376.2.c.a $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+4iq^{5}-q^{7}-q^{9}-6iq^{11}+\cdots$$
5376.2.c.b $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+4iq^{5}-q^{7}-q^{9}+2iq^{11}+\cdots$$
5376.2.c.c $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+2iq^{5}-q^{7}-q^{9}+4iq^{11}+\cdots$$
5376.2.c.d $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+2iq^{5}-q^{7}-q^{9}-6iq^{13}+\cdots$$
5376.2.c.e $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+2iq^{5}-q^{7}-q^{9}-4iq^{11}+\cdots$$
5376.2.c.f $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+2iq^{5}-q^{7}-q^{9}+2iq^{13}+\cdots$$
5376.2.c.g $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}-q^{7}-q^{9}-2iq^{11}-6q^{17}+\cdots$$
5376.2.c.h $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}-q^{7}-q^{9}-2iq^{11}+4iq^{13}+\cdots$$
5376.2.c.i $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}-q^{7}-q^{9}+6iq^{11}+2iq^{13}+\cdots$$
5376.2.c.j $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}-q^{7}-q^{9}-2iq^{11}-2iq^{13}+\cdots$$
5376.2.c.k $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}-q^{7}-q^{9}+6iq^{11}-4iq^{13}+\cdots$$
5376.2.c.l $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+2iq^{5}-q^{7}-q^{9}+4iq^{11}+\cdots$$
5376.2.c.m $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+2iq^{5}-q^{7}-q^{9}-4iq^{11}+\cdots$$
5376.2.c.n $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+2iq^{5}-q^{7}-q^{9}+2q^{15}+\cdots$$
5376.2.c.o $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{13}+\cdots$$
5376.2.c.p $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+4iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots$$
5376.2.c.q $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+4iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots$$
5376.2.c.r $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+2iq^{5}+q^{7}-q^{9}-4iq^{11}+\cdots$$
5376.2.c.s $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+2iq^{5}+q^{7}-q^{9}+4iq^{11}+\cdots$$
5376.2.c.t $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+2iq^{5}+q^{7}-q^{9}-2q^{15}+\cdots$$
5376.2.c.u $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+2iq^{5}+q^{7}-q^{9}-2iq^{13}+\cdots$$
5376.2.c.v $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+q^{7}-q^{9}-2iq^{11}-6q^{17}+\cdots$$
5376.2.c.w $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+q^{7}-q^{9}-2iq^{11}-4iq^{13}+\cdots$$
5376.2.c.x $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+q^{7}-q^{9}+6iq^{11}-2iq^{13}+\cdots$$
5376.2.c.y $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+q^{7}-q^{9}-2iq^{11}+2iq^{13}+\cdots$$
5376.2.c.z $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+q^{7}-q^{9}-6iq^{11}-4iq^{13}+\cdots$$
5376.2.c.ba $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+2iq^{5}+q^{7}-q^{9}-4iq^{11}+\cdots$$
5376.2.c.bb $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+2iq^{5}+q^{7}-q^{9}-6iq^{13}+\cdots$$
5376.2.c.bc $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+2iq^{5}+q^{7}-q^{9}+4iq^{11}+\cdots$$
5376.2.c.bd $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{13}+\cdots$$
5376.2.c.be $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+4iq^{5}+q^{7}-q^{9}+6iq^{11}+\cdots$$
5376.2.c.bf $2$ $42.928$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+4iq^{5}+q^{7}-q^{9}-2iq^{11}+\cdots$$
5376.2.c.bg $4$ $42.928$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-q^{7}-q^{9}+(2\zeta_{8}+\cdots)q^{11}+\cdots$$
5376.2.c.bh $4$ $42.928$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots$$
5376.2.c.bi $4$ $42.928$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots$$
5376.2.c.bj $4$ $42.928$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots$$
5376.2.c.bk $4$ $42.928$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots$$
5376.2.c.bl $4$ $42.928$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots$$
5376.2.c.bm $4$ $42.928$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+q^{7}-q^{9}+(-2\zeta_{8}+\cdots)q^{11}+\cdots$$
5376.2.c.bn $4$ $42.928$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(5376, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(5376, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(256, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(384, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(448, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(672, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(768, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(896, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1344, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1792, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2688, [\chi])$$$$^{\oplus 2}$$