# Properties

 Label 2541.2.w Level 2541 Weight 2 Character orbit w Rep. character $$\chi_{2541}(118,\cdot)$$ Character field $$\Q(\zeta_{10})$$ Dimension 576 Sturm bound 704

# Related objects

## Defining parameters

 Level: $$N$$ = $$2541 = 3 \cdot 7 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 2541.w (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$77$$ Character field: $$\Q(\zeta_{10})$$ Sturm bound: $$704$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2541, [\chi])$$.

Total New Old
Modular forms 1504 576 928
Cusp forms 1312 576 736
Eisenstein series 192 0 192

## Trace form

 $$576q + 148q^{4} - 10q^{7} + 20q^{8} + 144q^{9} + O(q^{10})$$ $$576q + 148q^{4} - 10q^{7} + 20q^{8} + 144q^{9} - 20q^{14} + 12q^{15} - 160q^{16} - 10q^{18} + 24q^{23} + 116q^{25} + 30q^{28} + 40q^{29} + 40q^{35} - 148q^{36} - 24q^{37} - 2q^{42} + 70q^{46} + 58q^{49} + 40q^{51} + 56q^{53} - 112q^{56} - 6q^{58} + 48q^{60} - 10q^{63} + 132q^{64} + 40q^{67} + 10q^{70} - 100q^{71} + 10q^{72} - 80q^{74} + 120q^{78} - 40q^{79} - 144q^{81} - 60q^{84} + 40q^{85} + 78q^{86} - 10q^{91} - 18q^{92} + 92q^{93} - 20q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2541, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(2541, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2541, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(847, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database