# Properties

 Label 1089.3.c Level $1089$ Weight $3$ Character orbit 1089.c Rep. character $\chi_{1089}(604,\cdot)$ Character field $\Q$ Dimension $86$ Newform subspaces $13$ Sturm bound $396$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1089 = 3^{2} \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1089.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q$$ Newform subspaces: $$13$$ Sturm bound: $$396$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1089, [\chi])$$.

Total New Old
Modular forms 288 94 194
Cusp forms 240 86 154
Eisenstein series 48 8 40

## Trace form

 $$86 q - 168 q^{4} + 6 q^{5} + O(q^{10})$$ $$86 q - 168 q^{4} + 6 q^{5} + 8 q^{14} + 332 q^{16} - 140 q^{20} - 34 q^{23} + 300 q^{25} + 184 q^{26} - 6 q^{31} - 174 q^{34} - 74 q^{37} - 74 q^{38} + 216 q^{47} - 286 q^{49} - 112 q^{53} + 324 q^{56} - 52 q^{58} + 144 q^{59} - 180 q^{64} + 136 q^{67} - 384 q^{70} - 366 q^{71} + 860 q^{80} - 14 q^{82} - 278 q^{86} + 300 q^{89} - 788 q^{91} + 564 q^{92} + 412 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1089, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1089.3.c.a $2$ $29.673$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$14$$ $$0$$ $$q+\beta q^{2}+2q^{4}+7q^{5}-5\beta q^{7}+6\beta q^{8}+\cdots$$
1089.3.c.b $4$ $29.673$ $$\Q(\sqrt{-2}, \sqrt{-11})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}-7q^{4}-2\beta _{1}q^{5}+7\beta _{2}q^{7}+\cdots$$
1089.3.c.c $4$ $29.673$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+2\beta _{1}q^{2}+(-4+4\beta _{2})q^{4}+(2-2\beta _{2}+\cdots)q^{5}+\cdots$$
1089.3.c.d $4$ $29.673$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-2\beta _{1}+\beta _{3})q^{2}+(-2+3\beta _{2})q^{4}+\cdots$$
1089.3.c.e $4$ $29.673$ $$\Q(\zeta_{10})$$ None $$0$$ $$0$$ $$-16$$ $$0$$ $$q+(\zeta_{10}-\zeta_{10}^{3})q^{2}+(1+4\zeta_{10}^{2})q^{4}+\cdots$$
1089.3.c.f $4$ $29.673$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+q^{4}-2\beta _{3}q^{5}-5\beta _{1}q^{7}+\cdots$$
1089.3.c.g $4$ $29.673$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2+3\beta _{2})q^{5}+\cdots$$
1089.3.c.h $4$ $29.673$ $$\Q(\sqrt{-2}, \sqrt{3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+4q^{4}+(-3\beta _{1}-\beta _{2})q^{7}+(-5\beta _{1}+\cdots)q^{13}+\cdots$$
1089.3.c.i $8$ $29.673$ 8.0.$$\cdots$$.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(-4+\beta _{2})q^{4}+(-\beta _{3}+\beta _{7})q^{5}+\cdots$$
1089.3.c.j $8$ $29.673$ 8.0.$$\cdots$$.15 None $$0$$ $$0$$ $$-16$$ $$0$$ $$q+(\beta _{1}+\beta _{4})q^{2}+(-3-\beta _{6})q^{4}+(-2+\cdots)q^{5}+\cdots$$
1089.3.c.k $8$ $29.673$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{1}q^{2}+(-3+\beta _{4}+\beta _{5})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$$
1089.3.c.l $16$ $29.673$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+(-3+\beta _{2})q^{4}+\beta _{8}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
1089.3.c.m $16$ $29.673$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{6}q^{2}+(-1+\beta _{2}-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1089, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1089, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(11, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(99, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(121, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(363, [\chi])$$$$^{\oplus 2}$$