# Properties

 Label 2736.3.o Level $2736$ Weight $3$ Character orbit 2736.o Rep. character $\chi_{2736}(721,\cdot)$ Character field $\Q$ Dimension $99$ Newform subspaces $18$ Sturm bound $1440$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 2736.o (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$18$$ Sturm bound: $$1440$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(2736, [\chi])$$.

Total New Old
Modular forms 984 101 883
Cusp forms 936 99 837
Eisenstein series 48 2 46

## Trace form

 $$99 q + 2 q^{5} + 18 q^{7} + O(q^{10})$$ $$99 q + 2 q^{5} + 18 q^{7} - 2 q^{11} + 26 q^{17} - 31 q^{19} + 22 q^{23} + 473 q^{25} - 148 q^{35} - 62 q^{43} - 98 q^{47} + 713 q^{49} + 76 q^{55} - 18 q^{61} - 106 q^{73} + 20 q^{77} + 78 q^{83} + 140 q^{85} - 274 q^{95} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(2736, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2736.3.o.a $1$ $74.551$ $$\Q$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$9$$ $$5$$ $$q+9q^{5}+5q^{7}+3q^{11}-15q^{17}+19q^{19}+\cdots$$
2736.3.o.b $2$ $74.551$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$-14$$ $$-22$$ $$q-7q^{5}-11q^{7}+3q^{11}+2\beta q^{13}+\cdots$$
2736.3.o.c $2$ $74.551$ $$\Q(\sqrt{57})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$-9$$ $$-5$$ $$q+(-4-\beta )q^{5}+(-4+3\beta )q^{7}+(-4+\cdots)q^{11}+\cdots$$
2736.3.o.d $2$ $74.551$ $$\Q(\sqrt{-13})$$ None $$0$$ $$0$$ $$-8$$ $$10$$ $$q-4q^{5}+5q^{7}-10q^{11}-\beta q^{13}-15q^{17}+\cdots$$
2736.3.o.e $2$ $74.551$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-8$$ $$20$$ $$q-4q^{5}+10q^{7}+10q^{11}-7\zeta_{6}q^{13}+\cdots$$
2736.3.o.f $2$ $74.551$ $$\Q(\sqrt{19})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$0$$ $$-10$$ $$q+\beta q^{5}-5q^{7}+5\beta q^{11}+7\beta q^{17}+\cdots$$
2736.3.o.g $2$ $74.551$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$4$$ $$q+2q^{7}-\zeta_{6}q^{13}+(13-\zeta_{6})q^{19}-5^{2}q^{25}+\cdots$$
2736.3.o.h $2$ $74.551$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$2$$ $$-10$$ $$q+q^{5}-5q^{7}+5q^{11}-2\beta q^{13}+5^{2}q^{17}+\cdots$$
2736.3.o.i $2$ $74.551$ $$\Q(\sqrt{-29})$$ None $$0$$ $$0$$ $$8$$ $$2$$ $$q+4q^{5}+q^{7}+14q^{11}+\beta q^{13}-23q^{17}+\cdots$$
2736.3.o.j $4$ $74.551$ $$\Q(\sqrt{-7}, \sqrt{10})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{1}q^{5}+2q^{7}+2\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots$$
2736.3.o.k $4$ $74.551$ $$\Q(\sqrt{3}, \sqrt{19})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$0$$ $$10$$ $$q+\beta _{1}q^{5}+(3+\beta _{3})q^{7}+\beta _{2}q^{11}+(2\beta _{1}+\cdots)q^{17}+\cdots$$
2736.3.o.l $4$ $74.551$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$10$$ $$-34$$ $$q+(3+\beta _{1})q^{5}+(-9-\beta _{1})q^{7}+(-3+\cdots)q^{11}+\cdots$$
2736.3.o.m $6$ $74.551$ 6.0.219615408.1 None $$0$$ $$0$$ $$2$$ $$2$$ $$q+\beta _{3}q^{5}+\beta _{2}q^{7}+(-4-\beta _{2})q^{11}+\cdots$$
2736.3.o.n $8$ $74.551$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$-4$$ $$12$$ $$q+(-1-\beta _{1}-\beta _{3})q^{5}+(1-\beta _{3})q^{7}+\cdots$$
2736.3.o.o $8$ $74.551$ 8.0.$$\cdots$$.9 None $$0$$ $$0$$ $$0$$ $$-12$$ $$q-\beta _{1}q^{5}+(-1-\beta _{7})q^{7}+(-\beta _{1}-\beta _{5}+\cdots)q^{11}+\cdots$$
2736.3.o.p $8$ $74.551$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$14$$ $$6$$ $$q+(2+\beta _{4})q^{5}+(1-\beta _{3})q^{7}+(-4-\beta _{4}+\cdots)q^{11}+\cdots$$
2736.3.o.q $20$ $74.551$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q+\beta _{10}q^{5}+(1-\beta _{3})q^{7}+\beta _{14}q^{11}+\cdots$$
2736.3.o.r $20$ $74.551$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q-\beta _{4}q^{5}+(1+\beta _{3})q^{7}+(1+\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(2736, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(2736, [\chi]) \simeq$$ $$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 15}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(456, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(684, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(912, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(1368, [\chi])$$$$^{\oplus 2}$$