Properties

 Label 912.3.be Level $912$ Weight $3$ Character orbit 912.be Rep. character $\chi_{912}(145,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $10$ Sturm bound $480$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 912.be (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$10$$ Sturm bound: $$480$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$7$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(912, [\chi])$$.

Total New Old
Modular forms 664 80 584
Cusp forms 616 80 536
Eisenstein series 48 0 48

Trace form

 $$80 q - 16 q^{7} + 120 q^{9} + O(q^{10})$$ $$80 q - 16 q^{7} + 120 q^{9} - 16 q^{19} + 48 q^{23} - 200 q^{25} - 192 q^{35} + 48 q^{39} - 48 q^{41} + 16 q^{43} + 96 q^{47} + 640 q^{49} + 144 q^{51} - 48 q^{53} - 96 q^{55} - 24 q^{57} + 16 q^{61} - 24 q^{63} - 384 q^{67} - 144 q^{71} - 40 q^{73} - 160 q^{77} + 168 q^{79} - 360 q^{81} + 160 q^{83} + 96 q^{85} + 576 q^{87} - 288 q^{89} + 96 q^{91} - 96 q^{93} + 416 q^{95} - 144 q^{97} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(912, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
912.3.be.a $2$ $24.850$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$-6$$ $$10$$ $$q+(-1-\zeta_{6})q^{3}+(-6+6\zeta_{6})q^{5}+5q^{7}+\cdots$$
912.3.be.b $2$ $24.850$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$2$$ $$-22$$ $$q+(-1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}-11q^{7}+\cdots$$
912.3.be.c $2$ $24.850$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$2$$ $$2$$ $$q+(-1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}+q^{7}+\cdots$$
912.3.be.d $6$ $24.850$ 6.0.6967728.1 None $$0$$ $$-9$$ $$-2$$ $$-26$$ $$q+(-2-\beta _{3})q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(-4+\cdots)q^{7}+\cdots$$
912.3.be.e $6$ $24.850$ 6.0.954288.1 None $$0$$ $$9$$ $$4$$ $$-10$$ $$q+(2-\beta _{2})q^{3}+(\beta _{1}+2\beta _{2}-\beta _{4}+\beta _{5})q^{5}+\cdots$$
912.3.be.f $6$ $24.850$ 6.0.92607408.1 None $$0$$ $$9$$ $$4$$ $$22$$ $$q+(1+\beta _{3})q^{3}+(2-\beta _{1}-\beta _{2}-2\beta _{3}+\cdots)q^{5}+\cdots$$
912.3.be.g $8$ $24.850$ 8.0.$$\cdots$$.10 None $$0$$ $$-12$$ $$4$$ $$24$$ $$q+(-1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{4})q^{5}+\cdots$$
912.3.be.h $8$ $24.850$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$12$$ $$-8$$ $$0$$ $$q+(2+\beta _{4})q^{3}+(2\beta _{4}-\beta _{5}-\beta _{7})q^{5}+\cdots$$
912.3.be.i $20$ $24.850$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$-30$$ $$0$$ $$4$$ $$q+(-1-\beta _{3})q^{3}+(-\beta _{2}-\beta _{13})q^{5}+\cdots$$
912.3.be.j $20$ $24.850$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$30$$ $$0$$ $$-20$$ $$q+(1+\beta _{3})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{15}+\cdots)q^{7}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(912, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(912, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(456, [\chi])$$$$^{\oplus 2}$$