Properties

 Label 900.3.f Level $900$ Weight $3$ Character orbit 900.f Rep. character $\chi_{900}(199,\cdot)$ Character field $\Q$ Dimension $88$ Newform subspaces $9$ Sturm bound $540$ Trace bound $26$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 900.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$540$$ Trace bound: $$26$$ Distinguishing $$T_p$$: $$7$$, $$29$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(900, [\chi])$$.

Total New Old
Modular forms 384 92 292
Cusp forms 336 88 248
Eisenstein series 48 4 44

Trace form

 $$88q + 6q^{4} + O(q^{10})$$ $$88q + 6q^{4} - 16q^{14} + 42q^{16} + 68q^{26} + 24q^{29} + 214q^{34} - 80q^{41} + 338q^{44} - 4q^{46} + 504q^{49} + 44q^{56} + 80q^{61} - 42q^{64} - 500q^{74} + 306q^{76} + 340q^{86} + 128q^{89} + 624q^{94} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(900, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
900.3.f.a $$2$$ $$24.523$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-4q^{4}+4iq^{8}-5iq^{13}+2^{4}q^{16}+\cdots$$
900.3.f.b $$2$$ $$24.523$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-4q^{4}-4iq^{8}-5iq^{13}+2^{4}q^{16}+\cdots$$
900.3.f.c $$4$$ $$24.523$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(2+\zeta_{12}^{3})q^{4}+(-4\zeta_{12}+\cdots)q^{7}+\cdots$$
900.3.f.d $$8$$ $$24.523$$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(-1-\beta _{1})q^{4}+(-2\beta _{4}+2\beta _{7})q^{7}+\cdots$$
900.3.f.e $$8$$ $$24.523$$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}q^{2}+(1+\zeta_{20}^{4})q^{4}+(-3\zeta_{20}+\cdots)q^{7}+\cdots$$
900.3.f.f $$16$$ $$24.523$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+(-1-\beta _{8})q^{4}+(-\beta _{11}-\beta _{13}+\cdots)q^{7}+\cdots$$
900.3.f.g $$16$$ $$24.523$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{11}q^{7}+\cdots$$
900.3.f.h $$16$$ $$24.523$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(1+\beta _{5})q^{4}+(\beta _{3}-\beta _{4}-\beta _{8}+\cdots)q^{7}+\cdots$$
900.3.f.i $$16$$ $$24.523$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{10}q^{2}+(2-\beta _{5})q^{4}-\beta _{8}q^{7}+(2\beta _{10}+\cdots)q^{8}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(900, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(900, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 2}$$