# Properties

 Label 1694.2.bb Level $1694$ Weight $2$ Character orbit 1694.bb Rep. character $\chi_{1694}(13,\cdot)$ Character field $\Q(\zeta_{110})$ Dimension $3520$ Sturm bound $528$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1694 = 2 \cdot 7 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1694.bb (of order $$110$$ and degree $$40$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$847$$ Character field: $$\Q(\zeta_{110})$$ Sturm bound: $$528$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1694, [\chi])$$.

Total New Old
Modular forms 10720 3520 7200
Cusp forms 10400 3520 6880
Eisenstein series 320 0 320

## Trace form

 $$3520q - 88q^{4} - 10q^{7} + 892q^{9} + O(q^{10})$$ $$3520q - 88q^{4} - 10q^{7} + 892q^{9} - 40q^{11} - 24q^{14} + 68q^{15} + 88q^{16} + 40q^{22} + 32q^{23} - 100q^{25} + 10q^{28} + 20q^{29} + 60q^{35} + 96q^{36} + 116q^{37} + 20q^{39} - 10q^{42} + 16q^{44} - 96q^{49} + 104q^{51} + 36q^{53} - 8q^{56} - 80q^{57} + 48q^{58} + 16q^{60} + 70q^{63} - 88q^{64} + 72q^{67} - 8q^{70} - 104q^{71} - 40q^{72} - 40q^{74} - 40q^{77} + 32q^{78} - 236q^{79} - 940q^{81} - 20q^{84} + 300q^{85} - 36q^{86} - 16q^{88} + 46q^{91} + 204q^{92} - 140q^{93} + 76q^{95} + 88q^{98} + 288q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1694, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1694, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1694, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(847, [\chi])$$$$^{\oplus 2}$$