# Properties

 Label 2496.2.c Level $2496$ Weight $2$ Character orbit 2496.c Rep. character $\chi_{2496}(961,\cdot)$ Character field $\Q$ Dimension $56$ Newform subspaces $18$ Sturm bound $896$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2496 = 2^{6} \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2496.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$18$$ Sturm bound: $$896$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$11$$, $$23$$, $$43$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2496, [\chi])$$.

Total New Old
Modular forms 472 56 416
Cusp forms 424 56 368
Eisenstein series 48 0 48

## Trace form

 $$56 q + 56 q^{9} + O(q^{10})$$ $$56 q + 56 q^{9} - 8 q^{13} + 16 q^{17} - 72 q^{25} - 56 q^{49} - 16 q^{61} - 16 q^{65} + 56 q^{81} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2496, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2496.2.c.a $2$ $19.931$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+2iq^{5}+iq^{7}+q^{9}+iq^{11}+\cdots$$
2496.2.c.b $2$ $19.931$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{5}-2iq^{7}+q^{9}-3iq^{11}+\cdots$$
2496.2.c.c $2$ $19.931$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}-iq^{7}+q^{9}+iq^{11}+(-3-i)q^{13}+\cdots$$
2496.2.c.d $2$ $19.931$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{11}+(1-\zeta_{6})q^{13}+\cdots$$
2496.2.c.e $2$ $19.931$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}-\zeta_{6}q^{5}+q^{9}+\zeta_{6}q^{11}+(1-\zeta_{6})q^{13}+\cdots$$
2496.2.c.f $2$ $19.931$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{5}+iq^{7}+q^{9}+(3-i)q^{13}+\cdots$$
2496.2.c.g $2$ $19.931$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{5}-iq^{7}+q^{9}+2iq^{11}+\cdots$$
2496.2.c.h $2$ $19.931$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+2iq^{5}-iq^{7}+q^{9}-iq^{11}+\cdots$$
2496.2.c.i $2$ $19.931$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{5}+2iq^{7}+q^{9}+3iq^{11}+\cdots$$
2496.2.c.j $2$ $19.931$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{7}+q^{9}-iq^{11}+(-3-i)q^{13}+\cdots$$
2496.2.c.k $2$ $19.931$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{11}+(1+\zeta_{6})q^{13}+\cdots$$
2496.2.c.l $2$ $19.931$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}-\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+(1-\zeta_{6})q^{13}+\cdots$$
2496.2.c.m $2$ $19.931$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{5}-iq^{7}+q^{9}+(3-i)q^{13}+\cdots$$
2496.2.c.n $2$ $19.931$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{5}+iq^{7}+q^{9}-2iq^{11}+\cdots$$
2496.2.c.o $6$ $19.931$ 6.0.153664.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$$
2496.2.c.p $6$ $19.931$ 6.0.153664.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$$
2496.2.c.q $8$ $19.931$ 8.0.134560000.4 None $$0$$ $$-8$$ $$0$$ $$0$$ $$q-q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+q^{9}+(\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots$$
2496.2.c.r $8$ $19.931$ 8.0.134560000.4 None $$0$$ $$8$$ $$0$$ $$0$$ $$q+q^{3}+\beta _{1}q^{5}+\beta _{6}q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2496, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2496, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(156, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(208, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(312, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(416, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(624, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(832, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1248, [\chi])$$$$^{\oplus 2}$$