Properties

 Label 2100.2.z Level 2100 Weight 2 Character orbit z Rep. character $$\chi_{2100}(421,\cdot)$$ Character field $$\Q(\zeta_{5})$$ Dimension 128 Sturm bound 960

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2100.z (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{5})$$ Sturm bound: $$960$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2100, [\chi])$$.

Total New Old
Modular forms 1968 128 1840
Cusp forms 1872 128 1744
Eisenstein series 96 0 96

Trace form

 $$128q - 4q^{5} - 32q^{9} + O(q^{10})$$ $$128q - 4q^{5} - 32q^{9} + 4q^{15} - 8q^{17} - 12q^{19} - 4q^{21} - 12q^{23} - 20q^{25} - 36q^{29} - 12q^{33} + 4q^{35} + 4q^{37} - 24q^{41} + 16q^{43} - 4q^{45} + 48q^{47} + 128q^{49} + 32q^{51} + 24q^{53} + 20q^{55} + 8q^{57} + 24q^{59} - 48q^{61} + 36q^{65} - 24q^{67} + 8q^{69} + 64q^{71} - 8q^{73} + 16q^{75} - 24q^{77} - 16q^{79} - 32q^{81} - 12q^{83} + 4q^{85} + 24q^{87} + 60q^{89} - 8q^{91} + 48q^{93} + 44q^{95} - 28q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(2100, [\chi])$$ into newform subspaces

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

Decomposition of $$S_{2}^{\mathrm{old}}(2100, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(700, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database