Properties

 Label 1040.2.da Level $1040$ Weight $2$ Character orbit 1040.da Rep. character $\chi_{1040}(641,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $56$ Newform subspaces $6$ Sturm bound $336$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1040 = 2^{4} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1040.da (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$336$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$

Dimensions

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

Total New Old
Modular forms 360 56 304
Cusp forms 312 56 256
Eisenstein series 48 0 48

Trace form

 $$56 q + 4 q^{3} - 12 q^{7} - 28 q^{9} + O(q^{10})$$ $$56 q + 4 q^{3} - 12 q^{7} - 28 q^{9} + 12 q^{23} - 56 q^{25} - 56 q^{27} + 12 q^{35} + 20 q^{39} + 4 q^{43} + 40 q^{49} + 24 q^{51} - 16 q^{53} - 8 q^{55} + 60 q^{59} + 8 q^{61} + 48 q^{63} + 4 q^{65} + 12 q^{67} + 16 q^{69} - 36 q^{71} - 4 q^{75} + 48 q^{77} - 16 q^{79} - 28 q^{81} - 36 q^{87} + 12 q^{89} - 16 q^{91} - 48 q^{93} + 16 q^{95} - 48 q^{97} + O(q^{100})$$

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.da.a $4$ $8.304$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{3}q^{5}+\cdots$$
1040.2.da.b $8$ $8.304$ 8.0.22581504.2 None $$0$$ $$-2$$ $$0$$ $$6$$ $$q+(\beta _{1}+\beta _{2}-\beta _{4}-2\beta _{6}-\beta _{7})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
1040.2.da.c $8$ $8.304$ 8.0.22581504.2 None $$0$$ $$2$$ $$0$$ $$-6$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{4}+2\beta _{6}+\beta _{7})q^{3}+\cdots$$
1040.2.da.d $8$ $8.304$ 8.0.22581504.2 None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(-\beta _{2}+\beta _{4}+\beta _{7})q^{3}+(\beta _{1}-\beta _{6})q^{5}+\cdots$$
1040.2.da.e $12$ $8.304$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$-6$$ $$q-\beta _{11}q^{3}-\beta _{5}q^{5}+(\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{7}+\cdots$$
1040.2.da.f $16$ $8.304$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$4$$ $$0$$ $$-6$$ $$q-\beta _{2}q^{3}+(\beta _{9}-\beta _{10})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1040, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(208, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(260, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(520, [\chi])$$$$^{\oplus 2}$$