Properties

 Label 525.2.bv Level 525 Weight 2 Character orbit bv Rep. character $$\chi_{525}(52,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 640 Newform subspaces 1 Sturm bound 160 Trace bound 0

Related objects

Defining parameters

 Level: $$N$$ = $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 525.bv (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$175$$ Character field: $$\Q(\zeta_{60})$$ Newform subspaces: $$1$$ Sturm bound: $$160$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(525, [\chi])$$.

Total New Old
Modular forms 1344 640 704
Cusp forms 1216 640 576
Eisenstein series 128 0 128

Trace form

 $$640q + 12q^{5} - 8q^{7} + 24q^{8} + O(q^{10})$$ $$640q + 12q^{5} - 8q^{7} + 24q^{8} + 12q^{10} + 8q^{15} - 80q^{16} - 72q^{22} + 48q^{23} - 12q^{25} - 36q^{28} - 80q^{29} + 32q^{30} - 24q^{32} + 36q^{33} - 64q^{35} + 160q^{36} - 4q^{37} - 192q^{38} - 12q^{40} - 16q^{42} + 120q^{43} + 60q^{47} + 288q^{50} - 432q^{52} - 136q^{53} - 16q^{57} - 4q^{58} - 240q^{59} - 20q^{60} - 4q^{63} + 120q^{64} + 4q^{65} - 8q^{67} - 132q^{68} + 76q^{70} - 12q^{72} - 36q^{73} - 48q^{75} - 60q^{77} - 80q^{78} + 12q^{80} - 80q^{81} - 252q^{82} - 160q^{84} + 72q^{85} + 24q^{87} + 152q^{88} + 56q^{92} - 96q^{93} + 172q^{95} - 488q^{98} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(525, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
525.2.bv.a $$640$$ $$4.192$$ None $$0$$ $$0$$ $$12$$ $$-8$$

Decomposition of $$S_{2}^{\mathrm{old}}(525, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(525, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 2}$$

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database