# Properties

 Label 684.3.bw Level $684$ Weight $3$ Character orbit 684.bw Rep. character $\chi_{684}(5,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $240$ Sturm bound $360$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$684 = 2^{2} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 684.bw (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$171$$ Character field: $$\Q(\zeta_{18})$$ Sturm bound: $$360$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(684, [\chi])$$.

Total New Old
Modular forms 1476 240 1236
Cusp forms 1404 240 1164
Eisenstein series 72 0 72

## Trace form

 $$240 q - 12 q^{3} - 12 q^{9} + O(q^{10})$$ $$240 q - 12 q^{3} - 12 q^{9} + 15 q^{13} + 6 q^{15} - 81 q^{17} - 21 q^{19} - 216 q^{23} + 30 q^{27} + 78 q^{33} + 24 q^{39} - 48 q^{43} - 342 q^{45} - 840 q^{49} + 93 q^{51} - 678 q^{57} + 135 q^{59} - 21 q^{61} + 12 q^{63} - 462 q^{67} + 234 q^{69} - 183 q^{73} - 102 q^{79} + 768 q^{81} + 108 q^{83} + 24 q^{87} + 648 q^{89} - 192 q^{91} - 408 q^{93} + 648 q^{95} + 180 q^{97} - 192 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(684, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{3}^{\mathrm{old}}(684, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(684, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 2}$$