# Properties

 Label 1755.2.i Level $1755$ Weight $2$ Character orbit 1755.i Rep. character $\chi_{1755}(586,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $96$ Newform subspaces $8$ Sturm bound $504$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1755 = 3^{3} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1755.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$8$$ Sturm bound: $$504$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$2$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1755, [\chi])$$.

Total New Old
Modular forms 528 96 432
Cusp forms 480 96 384
Eisenstein series 48 0 48

## Trace form

 $$96 q - 4 q^{2} - 48 q^{4} - 4 q^{5} + 24 q^{8} + O(q^{10})$$ $$96 q - 4 q^{2} - 48 q^{4} - 4 q^{5} + 24 q^{8} + 4 q^{11} + 24 q^{14} - 48 q^{16} - 24 q^{17} + 24 q^{19} - 12 q^{20} - 12 q^{22} + 12 q^{23} - 48 q^{25} + 12 q^{29} - 68 q^{32} + 24 q^{38} + 12 q^{40} + 8 q^{41} - 12 q^{43} - 112 q^{44} - 40 q^{47} - 60 q^{49} - 4 q^{50} - 32 q^{53} + 40 q^{56} + 24 q^{59} - 12 q^{61} + 176 q^{62} + 72 q^{64} - 8 q^{65} - 12 q^{67} + 48 q^{68} - 12 q^{70} + 64 q^{71} + 72 q^{73} - 48 q^{74} - 24 q^{76} - 28 q^{77} + 56 q^{80} + 24 q^{82} - 4 q^{86} - 36 q^{88} - 8 q^{89} + 68 q^{92} - 12 q^{94} - 36 q^{97} - 152 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1755, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1755.2.i.a $2$ $14.014$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-1$$ $$0$$ $$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$$
1755.2.i.b $2$ $14.014$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-1$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$$
1755.2.i.c $2$ $14.014$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-1$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$$
1755.2.i.d $2$ $14.014$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$4$$ $$q+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}-\zeta_{6}q^{13}+\cdots$$
1755.2.i.e $16$ $14.014$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-1$$ $$0$$ $$8$$ $$6$$ $$q-\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{4}+\beta _{12})q^{4}+\cdots$$
1755.2.i.f $16$ $14.014$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$3$$ $$0$$ $$-8$$ $$11$$ $$q+(-\beta _{1}+\beta _{6})q^{2}+(-1+\beta _{2}-\beta _{11}+\cdots)q^{4}+\cdots$$
1755.2.i.g $26$ $14.014$ None $$-1$$ $$0$$ $$13$$ $$-10$$
1755.2.i.h $30$ $14.014$ None $$-1$$ $$0$$ $$-15$$ $$-10$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1755, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1755, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(117, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(351, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(585, [\chi])$$$$^{\oplus 2}$$