Properties

 Label 585.2.bu Level $585$ Weight $2$ Character orbit 585.bu Rep. character $\chi_{585}(316,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $48$ Newform subspaces $5$ Sturm bound $168$ Trace bound $4$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 585.bu (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$168$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(585, [\chi])$$.

Total New Old
Modular forms 184 48 136
Cusp forms 152 48 104
Eisenstein series 32 0 32

Trace form

 $$48 q + 26 q^{4} + 6 q^{7} + O(q^{10})$$ $$48 q + 26 q^{4} + 6 q^{7} - 2 q^{10} - 12 q^{13} + 4 q^{14} - 34 q^{16} + 14 q^{17} + 12 q^{19} + 12 q^{20} + 12 q^{22} + 14 q^{23} - 48 q^{25} + 22 q^{26} + 78 q^{28} - 66 q^{32} - 6 q^{35} - 18 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} + 2 q^{43} - 18 q^{46} + 4 q^{49} + 58 q^{52} + 56 q^{53} + 16 q^{55} - 28 q^{56} - 60 q^{58} + 12 q^{59} - 8 q^{61} + 48 q^{62} - 200 q^{64} - 12 q^{65} - 54 q^{67} - 10 q^{68} - 48 q^{71} - 6 q^{74} + 30 q^{76} - 4 q^{77} - 24 q^{79} - 52 q^{82} + 18 q^{85} + 38 q^{88} - 48 q^{89} + 16 q^{91} - 52 q^{92} + 24 q^{94} + 24 q^{95} + 78 q^{97} + 24 q^{98} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(585, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
585.2.bu.a $$4$$ $$4.671$$ $$\Q(\zeta_{12})$$ None $$6$$ $$0$$ $$0$$ $$-12$$ $$q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(2+\cdots)q^{4}+\cdots$$
585.2.bu.b $$8$$ $$4.671$$ 8.0.56070144.2 None $$-6$$ $$0$$ $$0$$ $$6$$ $$q+(-1-\beta _{2}+\beta _{5}+\beta _{6})q^{2}+(2-\beta _{1}+\cdots)q^{4}+\cdots$$
585.2.bu.c $$8$$ $$4.671$$ 8.0.22581504.2 None $$0$$ $$0$$ $$0$$ $$-6$$ $$q+(\beta _{3}+\beta _{5}+\beta _{7})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
585.2.bu.d $$8$$ $$4.671$$ 8.0.191102976.5 None $$0$$ $$0$$ $$0$$ $$12$$ $$q+(2\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(-2\beta _{2}+\cdots)q^{4}+\cdots$$
585.2.bu.e $$20$$ $$4.671$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$6$$ $$q+\beta _{1}q^{2}+(\beta _{2}+\beta _{5}-\beta _{7})q^{4}+(\beta _{6}-\beta _{16}+\cdots)q^{5}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(585, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(585, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(117, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 2}$$