Properties

 Label 1040.2.f Level $1040$ Weight $2$ Character orbit 1040.f Rep. character $\chi_{1040}(129,\cdot)$ Character field $\Q$ Dimension $40$ Newform subspaces $7$ Sturm bound $336$ Trace bound $5$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1040 = 2^{4} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1040.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$336$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$37$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1040, [\chi])$$.

Total New Old
Modular forms 180 44 136
Cusp forms 156 40 116
Eisenstein series 24 4 20

Trace form

 $$40 q - 40 q^{9} + O(q^{10})$$ $$40 q - 40 q^{9} - 4 q^{25} - 8 q^{29} + 12 q^{35} + 8 q^{39} + 32 q^{49} + 40 q^{51} - 40 q^{55} - 24 q^{61} - 20 q^{65} + 8 q^{69} + 4 q^{75} - 64 q^{79} + 64 q^{81} + 48 q^{91} - 16 q^{95} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(1040, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1040.2.f.a $2$ $8.304$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1-i)q^{5}-q^{9}+iq^{11}+\cdots$$
1040.2.f.b $2$ $8.304$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1+i)q^{5}-q^{9}-iq^{11}+(-3+\cdots)q^{13}+\cdots$$
1040.2.f.c $4$ $8.304$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$0$$ $$-3$$ $$2$$ $$q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots$$
1040.2.f.d $4$ $8.304$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$0$$ $$3$$ $$-2$$ $$q-\beta _{2}q^{3}+(1-\beta _{1})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$$
1040.2.f.e $8$ $8.304$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{4}q^{5}+(-\beta _{4}+\beta _{7})q^{7}+\cdots$$
1040.2.f.f $10$ $8.304$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$-3$$ $$-2$$ $$q-\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$$
1040.2.f.g $10$ $8.304$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$3$$ $$2$$ $$q-\beta _{3}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(1040, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1040, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(260, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(520, [\chi])$$$$^{\oplus 2}$$