# Properties

 Label 1734.2.b Level $1734$ Weight $2$ Character orbit 1734.b Rep. character $\chi_{1734}(577,\cdot)$ Character field $\Q$ Dimension $46$ Newform subspaces $12$ Sturm bound $612$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1734 = 2 \cdot 3 \cdot 17^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1734.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$12$$ Sturm bound: $$612$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1734, [\chi])$$.

Total New Old
Modular forms 342 46 296
Cusp forms 270 46 224
Eisenstein series 72 0 72

## Trace form

 $$46 q - 2 q^{2} + 46 q^{4} - 2 q^{8} - 46 q^{9} + O(q^{10})$$ $$46 q - 2 q^{2} + 46 q^{4} - 2 q^{8} - 46 q^{9} + 16 q^{13} - 8 q^{15} + 46 q^{16} + 2 q^{18} - 4 q^{19} + 4 q^{21} - 54 q^{25} + 12 q^{26} - 4 q^{30} - 2 q^{32} + 4 q^{33} - 46 q^{36} + 8 q^{38} + 4 q^{42} - 20 q^{43} - 8 q^{47} - 62 q^{49} + 6 q^{50} + 16 q^{52} + 4 q^{53} + 8 q^{55} - 16 q^{59} - 8 q^{60} + 46 q^{64} - 4 q^{67} - 8 q^{69} - 16 q^{70} + 2 q^{72} - 4 q^{76} - 8 q^{77} + 46 q^{81} + 24 q^{83} + 4 q^{84} + 8 q^{87} - 4 q^{89} + 20 q^{93} - 24 q^{94} + 2 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1734, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1734.2.b.a $2$ $13.846$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+iq^{3}+q^{4}+4iq^{5}-iq^{6}+\cdots$$
1734.2.b.b $2$ $13.846$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-iq^{3}+q^{4}+2iq^{5}+iq^{6}+\cdots$$
1734.2.b.c $2$ $13.846$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-iq^{3}+q^{4}+3iq^{5}+iq^{6}+\cdots$$
1734.2.b.d $2$ $13.846$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+iq^{3}+q^{4}+4iq^{5}+iq^{6}+\cdots$$
1734.2.b.e $2$ $13.846$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+iq^{3}+q^{4}+iq^{6}+iq^{7}+q^{8}+\cdots$$
1734.2.b.f $2$ $13.846$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-iq^{3}+q^{4}-iq^{6}+2iq^{7}+\cdots$$
1734.2.b.g $2$ $13.846$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+iq^{3}+q^{4}+iq^{5}+iq^{6}+4iq^{7}+\cdots$$
1734.2.b.h $4$ $13.846$ $$\Q(\zeta_{8})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-\zeta_{8}q^{3}+q^{4}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots$$
1734.2.b.i $6$ $13.846$ 6.0.419904.1 None $$-6$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots$$
1734.2.b.j $6$ $13.846$ 6.0.419904.1 None $$6$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots$$
1734.2.b.k $8$ $13.846$ $$\Q(\zeta_{16})$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-\zeta_{16}q^{3}+q^{4}+(\zeta_{16}^{2}+\zeta_{16}^{3}+\cdots)q^{5}+\cdots$$
1734.2.b.l $8$ $13.846$ $$\Q(\zeta_{16})$$ None $$8$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-\zeta_{16}q^{3}+q^{4}+(2\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1734, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1734, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(51, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(102, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(289, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(578, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(867, [\chi])$$$$^{\oplus 2}$$