# Properties

 Label 18.7.b Level $18$ Weight $7$ Character orbit 18.b Rep. character $\chi_{18}(17,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $21$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 18.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$21$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(18, [\chi])$$.

Total New Old
Modular forms 22 2 20
Cusp forms 14 2 12
Eisenstein series 8 0 8

## Trace form

 $$2 q - 64 q^{4} - 968 q^{7} + O(q^{10})$$ $$2 q - 64 q^{4} - 968 q^{7} - 1968 q^{10} + 6736 q^{13} + 2048 q^{16} + 11488 q^{19} - 15168 q^{22} - 29266 q^{25} + 30976 q^{28} - 79592 q^{31} - 144 q^{34} + 105052 q^{37} + 62976 q^{40} + 7600 q^{43} + 38208 q^{46} + 233214 q^{49} - 215552 q^{52} - 466416 q^{55} - 332112 q^{58} + 26500 q^{61} - 65536 q^{64} + 337936 q^{67} + 952512 q^{70} + 472288 q^{73} - 367616 q^{76} - 70232 q^{79} + 419088 q^{82} - 4428 q^{85} + 485376 q^{88} - 3260224 q^{91} - 868800 q^{94} - 642848 q^{97} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(18, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.7.b.a $2$ $4.141$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-968$$ $$q+4\beta q^{2}-2^{5}q^{4}+123\beta q^{5}-22^{2}q^{7}+\cdots$$

## Decomposition of $$S_{7}^{\mathrm{old}}(18, [\chi])$$ into lower level spaces

$$S_{7}^{\mathrm{old}}(18, [\chi]) \cong$$ $$S_{7}^{\mathrm{new}}(3, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(6, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 2}$$