# Properties

 Label 3234.2.ca Level 3234 Weight 2 Character orbit ca Rep. character $$\chi_{3234}(13,\cdot)$$ Character field $$\Q(\zeta_{70})$$ Dimension 2688 Sturm bound 1344

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3234.ca (of order $$70$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$539$$ Character field: $$\Q(\zeta_{70})$$ Sturm bound: $$1344$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3234, [\chi])$$.

Total New Old
Modular forms 16320 2688 13632
Cusp forms 15936 2688 13248
Eisenstein series 384 0 384

## Trace form

 $$2688q - 112q^{4} + 20q^{7} - 112q^{9} + O(q^{10})$$ $$2688q - 112q^{4} + 20q^{7} - 112q^{9} + 12q^{11} + 4q^{14} + 30q^{15} + 112q^{16} + 140q^{17} + 56q^{20} + 18q^{22} - 16q^{23} - 120q^{25} + 56q^{26} - 10q^{28} - 40q^{29} - 20q^{35} + 112q^{36} + 40q^{37} + 56q^{38} + 70q^{40} - 18q^{42} - 52q^{44} - 56q^{45} + 308q^{47} + 88q^{49} + 200q^{51} - 56q^{53} - 126q^{55} - 40q^{56} + 50q^{58} - 56q^{59} + 20q^{60} + 140q^{62} + 20q^{63} - 112q^{64} + 4q^{70} + 48q^{71} + 420q^{73} + 80q^{74} - 20q^{77} + 120q^{79} + 112q^{81} - 40q^{85} - 180q^{86} - 76q^{88} - 56q^{89} + 136q^{91} + 16q^{92} + 32q^{93} - 140q^{94} + 40q^{95} + 16q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3234, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(3234, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3234, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(539, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1078, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1617, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database