# Properties

 Label 1232.2.q Level $1232$ Weight $2$ Character orbit 1232.q Rep. character $\chi_{1232}(177,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $80$ Newform subspaces $16$ Sturm bound $384$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1232 = 2^{4} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1232.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$16$$ Sturm bound: $$384$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1232, [\chi])$$.

Total New Old
Modular forms 408 80 328
Cusp forms 360 80 280
Eisenstein series 48 0 48

## Trace form

 $$80 q - 4 q^{3} - 4 q^{7} - 40 q^{9} + O(q^{10})$$ $$80 q - 4 q^{3} - 4 q^{7} - 40 q^{9} + 4 q^{19} + 8 q^{21} - 40 q^{25} + 32 q^{27} + 16 q^{29} + 28 q^{31} + 12 q^{35} + 4 q^{39} - 32 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 20 q^{51} - 16 q^{55} - 48 q^{57} - 44 q^{59} - 92 q^{63} + 16 q^{65} - 8 q^{67} - 32 q^{69} + 16 q^{71} + 8 q^{73} + 8 q^{75} + 28 q^{79} - 16 q^{81} + 40 q^{83} + 8 q^{89} + 48 q^{91} + 32 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1232, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1232.2.q.a $2$ $9.838$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$4$$ $$5$$ $$q+(-3+3\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
1232.2.q.b $2$ $9.838$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-2$$ $$-5$$ $$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
1232.2.q.c $2$ $9.838$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots$$
1232.2.q.d $2$ $9.838$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$1$$ $$q+(1-\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots$$
1232.2.q.e $2$ $9.838$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$-2$$ $$5$$ $$q+(3-3\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
1232.2.q.f $4$ $9.838$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$4$$ $$2$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots$$
1232.2.q.g $4$ $9.838$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
1232.2.q.h $4$ $9.838$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$-2$$ $$q+(1+\beta _{1}+\beta _{2})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$$
1232.2.q.i $6$ $9.838$ 6.0.64827.1 None $$0$$ $$-5$$ $$2$$ $$0$$ $$q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(1+\cdots)q^{5}+\cdots$$
1232.2.q.j $6$ $9.838$ 6.0.1783323.2 None $$0$$ $$-3$$ $$2$$ $$-2$$ $$q+(-1+\beta _{4}-\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots$$
1232.2.q.k $6$ $9.838$ 6.0.1783323.2 None $$0$$ $$-1$$ $$2$$ $$-2$$ $$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots$$
1232.2.q.l $6$ $9.838$ 6.0.309123.1 None $$0$$ $$1$$ $$2$$ $$-4$$ $$q+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots$$
1232.2.q.m $6$ $9.838$ $$\Q(\zeta_{18})$$ None $$0$$ $$3$$ $$-6$$ $$0$$ $$q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(-\zeta_{18}+\cdots)q^{5}+\cdots$$
1232.2.q.n $8$ $9.838$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$-2$$ $$4$$ $$1$$ $$q+(\beta _{2}-\beta _{4})q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots$$
1232.2.q.o $10$ $9.838$ 10.0.$$\cdots$$.1 None $$0$$ $$-1$$ $$-4$$ $$2$$ $$q+(\beta _{2}+\beta _{8})q^{3}+(-1+\beta _{3}+\beta _{4}+\beta _{7}+\cdots)q^{5}+\cdots$$
1232.2.q.p $10$ $9.838$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$3$$ $$-4$$ $$0$$ $$q+(-\beta _{4}-\beta _{7})q^{3}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1232, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1232, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(154, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(308, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(616, [\chi])$$$$^{\oplus 2}$$