Properties

 Label 900.3.c Level $900$ Weight $3$ Character orbit 900.c Rep. character $\chi_{900}(451,\cdot)$ Character field $\Q$ Dimension $92$ Newform subspaces $21$ Sturm bound $540$ Trace bound $13$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 900.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$21$$ Sturm bound: $$540$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$7$$, $$13$$, $$17$$

Dimensions

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

Total New Old
Modular forms 384 98 286
Cusp forms 336 92 244
Eisenstein series 48 6 42

Trace form

 $$92q + 2q^{4} - 12q^{8} + O(q^{10})$$ $$92q + 2q^{4} - 12q^{8} - 24q^{14} - 22q^{16} - 4q^{17} - 8q^{22} - 44q^{26} + 56q^{28} - 20q^{29} + 20q^{32} - 6q^{34} - 88q^{37} + 112q^{38} + 4q^{41} - 90q^{44} + 84q^{46} - 556q^{49} - 72q^{52} + 28q^{53} + 420q^{56} - 56q^{58} + 48q^{61} - 112q^{62} - 118q^{64} - 360q^{68} + 88q^{73} - 92q^{74} - 78q^{76} + 48q^{77} + 72q^{82} - 276q^{86} + 352q^{88} + 220q^{89} + 216q^{92} - 120q^{94} - 152q^{97} + 760q^{98} + O(q^{100})$$

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.c.a $$1$$ $$24.523$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$-2$$ $$0$$ $$0$$ $$0$$ $$q-2q^{2}+4q^{4}-8q^{8}-24q^{13}+2^{4}q^{16}+\cdots$$
900.3.c.b $$1$$ $$24.523$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$-2$$ $$0$$ $$0$$ $$0$$ $$q-2q^{2}+4q^{4}-8q^{8}+10q^{13}+2^{4}q^{16}+\cdots$$
900.3.c.c $$1$$ $$24.523$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$2$$ $$0$$ $$0$$ $$0$$ $$q+2q^{2}+4q^{4}+8q^{8}+10q^{13}+2^{4}q^{16}+\cdots$$
900.3.c.d $$1$$ $$24.523$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$2$$ $$0$$ $$0$$ $$0$$ $$q+2q^{2}+4q^{4}+8q^{8}+24q^{13}+2^{4}q^{16}+\cdots$$
900.3.c.e $$2$$ $$24.523$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(-2-2\zeta_{6})q^{4}-4\zeta_{6}q^{7}+\cdots$$
900.3.c.f $$2$$ $$24.523$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}-6\zeta_{6}q^{7}+\cdots$$
900.3.c.g $$2$$ $$24.523$$ $$\Q(\sqrt{-15})$$ $$\Q(\sqrt{-15})$$ $$-1$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{2}+(-4+\beta )q^{4}+(4+3\beta )q^{8}+\cdots$$
900.3.c.h $$2$$ $$24.523$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-4q^{4}+2iq^{7}+4iq^{8}+8q^{14}+\cdots$$
900.3.c.i $$2$$ $$24.523$$ $$\Q(\sqrt{-15})$$ $$\Q(\sqrt{-15})$$ $$1$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta )q^{2}+(-3-\beta )q^{4}+(-7+3\beta )q^{8}+\cdots$$
900.3.c.j $$2$$ $$24.523$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(-2-2\zeta_{6})q^{4}-6\zeta_{6}q^{7}+\cdots$$
900.3.c.k $$4$$ $$24.523$$ $$\Q(\zeta_{10})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{10}q^{2}+(-1+\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{4}+\cdots$$
900.3.c.l $$4$$ $$24.523$$ 4.0.8405.1 None $$-1$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3})q^{4}+(2\beta _{1}+\cdots)q^{7}+\cdots$$
900.3.c.m $$4$$ $$24.523$$ 4.0.8405.1 None $$1$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(2\beta _{1}+\cdots)q^{7}+\cdots$$
900.3.c.n $$8$$ $$24.523$$ 8.0.4069419264.1 None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(-1+\beta _{7})q^{4}+(-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots$$
900.3.c.o $$8$$ $$24.523$$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{3}-\beta _{7})q^{7}+\cdots$$
900.3.c.p $$8$$ $$24.523$$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+(1+\beta _{7})q^{4}-\beta _{2}q^{7}+(-\beta _{5}+\cdots)q^{8}+\cdots$$
900.3.c.q $$8$$ $$24.523$$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{4}q^{7}-\beta _{3}q^{8}+\cdots$$
900.3.c.r $$8$$ $$24.523$$ 8.0.6080256576.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(1+\beta _{7})q^{4}+(\beta _{2}+\beta _{4})q^{7}+\cdots$$
900.3.c.s $$8$$ $$24.523$$ 8.0.$$\cdots$$.9 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{5})q^{4}-\beta _{3}q^{7}+\cdots$$
900.3.c.t $$8$$ $$24.523$$ 8.0.4069419264.1 None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{5})q^{4}+\cdots$$
900.3.c.u $$8$$ $$24.523$$ 8.0.85100625.1 None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{5})q^{2}+(1-\beta _{4})q^{4}+(-1-\beta _{3}+\cdots)q^{7}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(900, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 2}$$