# 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 Newform subspaces 2 Sturm bound 160 Trace bound 1

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## 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: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ 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

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

## 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.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

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database