Properties

 Label 3150.2.dl Level 3150 Weight 2 Character orbit dl Rep. character $$\chi_{3150}(341,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 640 Sturm bound 1440

Related objects

Defining parameters

 Level: $$N$$ = $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3150.dl (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$525$$ Character field: $$\Q(\zeta_{30})$$ Sturm bound: $$1440$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3150, [\chi])$$.

Total New Old
Modular forms 5888 640 5248
Cusp forms 5632 640 4992
Eisenstein series 256 0 256

Trace form

 $$640q - 80q^{4} - 8q^{7} + O(q^{10})$$ $$640q - 80q^{4} - 8q^{7} - 12q^{10} + 80q^{16} - 32q^{22} + 4q^{25} - 12q^{28} - 36q^{31} - 16q^{37} - 12q^{40} - 32q^{43} + 24q^{46} + 8q^{49} + 8q^{58} + 160q^{64} - 32q^{67} - 108q^{70} + 192q^{73} - 8q^{79} + 384q^{82} - 80q^{85} + 4q^{88} - 104q^{91} + 96q^{94} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(3150, [\chi])$$ into newform subspaces

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

Decomposition of $$S_{2}^{\mathrm{old}}(3150, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3150, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1575, [\chi])$$$$^{\oplus 2}$$

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database