# Properties

 Label 1840.2.m Level $1840$ Weight $2$ Character orbit 1840.m Rep. character $\chi_{1840}(1839,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $7$ Sturm bound $576$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1840 = 2^{4} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1840.m (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$460$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$576$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1840, [\chi])$$.

Total New Old
Modular forms 300 72 228
Cusp forms 276 72 204
Eisenstein series 24 0 24

## Trace form

 $$72 q + 72 q^{9} + O(q^{10})$$ $$72 q + 72 q^{9} + 24 q^{29} + 24 q^{41} - 96 q^{49} + 36 q^{69} + 144 q^{81} - 72 q^{85} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1840, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1840.2.m.a $4$ $14.692$ $$\Q(\sqrt{6}, \sqrt{-14})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-q^{3}-\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots$$
1840.2.m.b $4$ $14.692$ $$\Q(\sqrt{5}, \sqrt{-23})$$ $$\Q(\sqrt{-115})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{5}-\beta _{2}q^{7}-3q^{9}+3\beta _{1}q^{17}+\cdots$$
1840.2.m.c $4$ $14.692$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{5}+3\beta _{2}q^{7}+\cdots$$
1840.2.m.d $4$ $14.692$ $$\Q(\sqrt{6}, \sqrt{-14})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+q^{3}+\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots$$
1840.2.m.e $8$ $14.692$ 8.0.$$\cdots$$.1 $$\Q(\sqrt{-115})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{5}+\beta _{7}q^{7}-3q^{9}+(-\beta _{1}+\beta _{4}+\cdots)q^{17}+\cdots$$
1840.2.m.f $8$ $14.692$ 8.0.40960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+\beta _{6}q^{5}+2\beta _{5}q^{7}+2q^{9}+\cdots$$
1840.2.m.g $40$ $14.692$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1840, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1840, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(460, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(920, [\chi])$$$$^{\oplus 2}$$