Properties

 Label 1040.2.d Level $1040$ Weight $2$ Character orbit 1040.d Rep. character $\chi_{1040}(209,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $6$ Sturm bound $336$ Trace bound $15$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1040 = 2^{4} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1040.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$336$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$3$$

Dimensions

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

Total New Old
Modular forms 180 36 144
Cusp forms 156 36 120
Eisenstein series 24 0 24

Trace form

 $$36 q - 36 q^{9} + O(q^{10})$$ $$36 q - 36 q^{9} - 12 q^{11} + 12 q^{15} + 20 q^{19} - 8 q^{21} + 8 q^{25} + 8 q^{29} + 4 q^{31} - 24 q^{35} - 8 q^{39} - 52 q^{49} - 8 q^{51} - 4 q^{55} + 36 q^{59} + 16 q^{61} - 8 q^{69} + 28 q^{71} - 44 q^{75} + 8 q^{79} + 44 q^{81} + 16 q^{85} - 8 q^{89} - 12 q^{91} - 36 q^{95} + 36 q^{99} + O(q^{100})$$

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.d.a $2$ $8.304$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2-i)q^{5}-4iq^{7}+3q^{9}+2q^{11}+\cdots$$
1040.2.d.b $6$ $8.304$ 6.0.3534400.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{4})q^{3}+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots$$
1040.2.d.c $6$ $8.304$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{4})q^{3}+(\beta _{1}+\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$$
1040.2.d.d $6$ $8.304$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$$
1040.2.d.e $6$ $8.304$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{3}+\beta _{4})q^{3}+(\beta _{1}-\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$$
1040.2.d.f $10$ $8.304$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\beta _{9}q^{3}+\beta _{2}q^{5}-\beta _{4}q^{7}+(-4-\beta _{5}+\cdots)q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1040, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(260, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(520, [\chi])$$$$^{\oplus 2}$$