# Properties

 Label 210.3.w Level 210 Weight 3 Character orbit w Rep. character $$\chi_{210}(17,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 128 Newform subspaces 2 Sturm bound 144 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$210 = 2 \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 210.w (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$105$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$144$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(210, [\chi])$$.

Total New Old
Modular forms 416 128 288
Cusp forms 352 128 224
Eisenstein series 64 0 64

## Trace form

 $$128q + 8q^{7} + O(q^{10})$$ $$128q + 8q^{7} + 48q^{10} + 24q^{15} + 256q^{16} - 32q^{18} + 72q^{21} + 32q^{22} - 32q^{25} + 16q^{28} + 48q^{30} + 60q^{33} + 32q^{36} - 64q^{37} - 224q^{42} + 64q^{43} - 588q^{45} - 48q^{46} - 168q^{51} - 536q^{57} + 112q^{58} + 32q^{60} + 1200q^{61} - 324q^{63} + 32q^{67} + 64q^{72} - 1248q^{73} - 96q^{75} - 256q^{78} - 128q^{81} - 384q^{82} - 304q^{85} - 612q^{87} - 32q^{88} - 464q^{91} - 372q^{93} - 96q^{96} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(210, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
210.3.w.a $$64$$ $$5.722$$ None $$-32$$ $$-6$$ $$-12$$ $$4$$
210.3.w.b $$64$$ $$5.722$$ None $$32$$ $$6$$ $$12$$ $$4$$

## Decomposition of $$S_{3}^{\mathrm{old}}(210, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(210, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database