Properties

 Label 1296.2.i Level $1296$ Weight $2$ Character orbit 1296.i Rep. character $\chi_{1296}(433,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $46$ Newform subspaces $20$ Sturm bound $432$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1296 = 2^{4} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1296.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$20$$ Sturm bound: $$432$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$7$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1296, [\chi])$$.

Total New Old
Modular forms 504 50 454
Cusp forms 360 46 314
Eisenstein series 144 4 140

Trace form

 $$46 q - 2 q^{7} + O(q^{10})$$ $$46 q - 2 q^{7} + 2 q^{13} + 4 q^{19} - 17 q^{25} - 32 q^{31} - 4 q^{37} - 32 q^{43} - 15 q^{49} + 24 q^{55} + 2 q^{61} - 2 q^{67} + 20 q^{73} - 2 q^{79} + 12 q^{85} + 92 q^{91} - 10 q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(1296, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1296.2.i.a $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-4$$ $$-3$$ $$q-4\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots$$
1296.2.i.b $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$-4$$ $$q-3\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\zeta_{6}q^{13}+\cdots$$
1296.2.i.c $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$-1$$ $$q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$$
1296.2.i.d $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$2$$ $$q-3\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$$
1296.2.i.e $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots$$
1296.2.i.f $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots$$
1296.2.i.g $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$3$$ $$q-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots$$
1296.2.i.h $2$ $10.349$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-4+4\zeta_{6})q^{7}-2\zeta_{6}q^{13}-8q^{19}+\cdots$$
1296.2.i.i $2$ $10.349$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-1$$ $$q+(-1+\zeta_{6})q^{7}-5\zeta_{6}q^{13}+7q^{19}+\cdots$$
1296.2.i.j $2$ $10.349$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$5$$ $$q+(5-5\zeta_{6})q^{7}+7\zeta_{6}q^{13}+q^{19}+(5+\cdots)q^{25}+\cdots$$
1296.2.i.k $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots$$
1296.2.i.l $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$3$$ $$q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots$$
1296.2.i.m $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots$$
1296.2.i.n $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$-4$$ $$q+3\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\zeta_{6}q^{13}+\cdots$$
1296.2.i.o $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$-1$$ $$q+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots$$
1296.2.i.p $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$2$$ $$q+3\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$$
1296.2.i.q $2$ $10.349$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$4$$ $$-3$$ $$q+4\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots$$
1296.2.i.r $4$ $10.349$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{7}+\cdots$$
1296.2.i.s $4$ $10.349$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{12}^{2}q^{5}+(2-2\zeta_{12})q^{7}+(-2\zeta_{12}^{2}+\cdots)q^{11}+\cdots$$
1296.2.i.t $4$ $10.349$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+2\zeta_{12}^{2}q^{7}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(1296, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1296, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(162, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(324, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(432, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(648, [\chi])$$$$^{\oplus 2}$$