# Properties

 Label 3.7.b Level $3$ Weight $7$ Character orbit 3.b Rep. character $\chi_{3}(2,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $2$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 3.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$2$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(3, [\chi])$$.

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

## Trace form

 $$q - 27 q^{3} + 64 q^{4} - 286 q^{7} + 729 q^{9} + O(q^{10})$$ $$q - 27 q^{3} + 64 q^{4} - 286 q^{7} + 729 q^{9} - 1728 q^{12} + 506 q^{13} + 4096 q^{16} - 10582 q^{19} + 7722 q^{21} + 15625 q^{25} - 19683 q^{27} - 18304 q^{28} + 35282 q^{31} + 46656 q^{36} - 89206 q^{37} - 13662 q^{39} + 111386 q^{43} - 110592 q^{48} - 35853 q^{49} + 32384 q^{52} + 285714 q^{57} - 420838 q^{61} - 208494 q^{63} + 262144 q^{64} + 172874 q^{67} + 638066 q^{73} - 421875 q^{75} - 677248 q^{76} - 204622 q^{79} + 531441 q^{81} + 494208 q^{84} - 144716 q^{91} - 952614 q^{93} - 56446 q^{97} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(3, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3.7.b.a $1$ $0.690$ $$\Q$$ $$\Q(\sqrt{-3})$$ $$0$$ $$-27$$ $$0$$ $$-286$$ $$q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots$$