Properties

 Label 525.2.z Level 525 Weight 2 Character orbit z Rep. character $$\chi_{525}(64,\cdot)$$ Character field $$\Q(\zeta_{10})$$ Dimension 128 Newforms 2 Sturm bound 160 Trace bound 1

Related objects

Defining parameters

 Level: $$N$$ = $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 525.z (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$25$$ Character field: $$\Q(\zeta_{10})$$ Newforms: $$2$$ Sturm bound: $$160$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

Dimensions

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

Total New Old
Modular forms 336 128 208
Cusp forms 304 128 176
Eisenstein series 32 0 32

Trace form

 $$128q$$ $$\mathstrut +\mathstrut 36q^{4}$$ $$\mathstrut -\mathstrut 4q^{5}$$ $$\mathstrut +\mathstrut 32q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$128q$$ $$\mathstrut +\mathstrut 36q^{4}$$ $$\mathstrut -\mathstrut 4q^{5}$$ $$\mathstrut +\mathstrut 32q^{9}$$ $$\mathstrut +\mathstrut 8q^{10}$$ $$\mathstrut -\mathstrut 4q^{15}$$ $$\mathstrut -\mathstrut 20q^{16}$$ $$\mathstrut -\mathstrut 12q^{19}$$ $$\mathstrut -\mathstrut 12q^{20}$$ $$\mathstrut -\mathstrut 4q^{21}$$ $$\mathstrut +\mathstrut 80q^{22}$$ $$\mathstrut -\mathstrut 20q^{23}$$ $$\mathstrut +\mathstrut 28q^{25}$$ $$\mathstrut -\mathstrut 24q^{26}$$ $$\mathstrut -\mathstrut 20q^{29}$$ $$\mathstrut -\mathstrut 8q^{30}$$ $$\mathstrut -\mathstrut 20q^{33}$$ $$\mathstrut +\mathstrut 24q^{34}$$ $$\mathstrut -\mathstrut 4q^{35}$$ $$\mathstrut -\mathstrut 36q^{36}$$ $$\mathstrut +\mathstrut 20q^{37}$$ $$\mathstrut +\mathstrut 16q^{39}$$ $$\mathstrut -\mathstrut 36q^{40}$$ $$\mathstrut -\mathstrut 8q^{41}$$ $$\mathstrut -\mathstrut 84q^{44}$$ $$\mathstrut +\mathstrut 4q^{45}$$ $$\mathstrut -\mathstrut 4q^{46}$$ $$\mathstrut -\mathstrut 80q^{47}$$ $$\mathstrut -\mathstrut 128q^{49}$$ $$\mathstrut +\mathstrut 148q^{50}$$ $$\mathstrut +\mathstrut 64q^{51}$$ $$\mathstrut +\mathstrut 40q^{53}$$ $$\mathstrut -\mathstrut 12q^{55}$$ $$\mathstrut -\mathstrut 80q^{58}$$ $$\mathstrut +\mathstrut 24q^{59}$$ $$\mathstrut +\mathstrut 4q^{60}$$ $$\mathstrut +\mathstrut 32q^{61}$$ $$\mathstrut -\mathstrut 100q^{62}$$ $$\mathstrut +\mathstrut 36q^{64}$$ $$\mathstrut +\mathstrut 116q^{65}$$ $$\mathstrut -\mathstrut 16q^{66}$$ $$\mathstrut -\mathstrut 40q^{67}$$ $$\mathstrut +\mathstrut 8q^{69}$$ $$\mathstrut -\mathstrut 8q^{70}$$ $$\mathstrut +\mathstrut 32q^{71}$$ $$\mathstrut -\mathstrut 40q^{73}$$ $$\mathstrut -\mathstrut 16q^{74}$$ $$\mathstrut -\mathstrut 16q^{75}$$ $$\mathstrut -\mathstrut 72q^{76}$$ $$\mathstrut +\mathstrut 40q^{77}$$ $$\mathstrut +\mathstrut 24q^{79}$$ $$\mathstrut -\mathstrut 44q^{80}$$ $$\mathstrut -\mathstrut 32q^{81}$$ $$\mathstrut +\mathstrut 60q^{83}$$ $$\mathstrut +\mathstrut 12q^{84}$$ $$\mathstrut -\mathstrut 76q^{85}$$ $$\mathstrut +\mathstrut 120q^{86}$$ $$\mathstrut -\mathstrut 80q^{87}$$ $$\mathstrut -\mathstrut 140q^{88}$$ $$\mathstrut -\mathstrut 36q^{89}$$ $$\mathstrut -\mathstrut 8q^{90}$$ $$\mathstrut -\mathstrut 16q^{91}$$ $$\mathstrut -\mathstrut 200q^{92}$$ $$\mathstrut +\mathstrut 12q^{94}$$ $$\mathstrut +\mathstrut 124q^{95}$$ $$\mathstrut +\mathstrut 20q^{96}$$ $$\mathstrut +\mathstrut 60q^{97}$$ $$\mathstrut +\mathstrut O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(525, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
525.2.z.a $$56$$ $$4.192$$ None $$0$$ $$0$$ $$-2$$ $$0$$
525.2.z.b $$72$$ $$4.192$$ None $$0$$ $$0$$ $$-2$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(525, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 2}$$