Properties

 Label 3150.2.df Level 3150 Weight 2 Character orbit df Rep. character $$\chi_{3150}(131,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 1920 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.df (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$1575$$ 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 5824 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

Trace form

 $$1920q + 480q^{4} + O(q^{10})$$ $$1920q + 480q^{4} - 26q^{15} - 480q^{16} + 36q^{17} + 8q^{18} + 12q^{21} - 24q^{23} - 36q^{27} + 2q^{30} - 30q^{35} - 4q^{39} - 28q^{42} - 96q^{45} + 12q^{50} + 24q^{51} + 80q^{57} - 12q^{58} - 14q^{60} + 108q^{62} - 50q^{63} + 480q^{64} + 144q^{68} - 126q^{69} - 24q^{70} - 8q^{72} + 180q^{75} - 144q^{77} - 16q^{78} - 24q^{79} + 44q^{81} + 18q^{84} + 36q^{87} - 90q^{89} + 72q^{90} - 36q^{92} + 112q^{93} + 32q^{99} + O(q^{100})$$

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database