Properties

 Label 392.6.i Level $392$ Weight $6$ Character orbit 392.i Rep. character $\chi_{392}(177,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $100$ Newform subspaces $18$ Sturm bound $336$ Trace bound $9$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$392 = 2^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 392.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$18$$ Sturm bound: $$336$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(392, [\chi])$$.

Total New Old
Modular forms 592 100 492
Cusp forms 528 100 428
Eisenstein series 64 0 64

Trace form

 $$100 q + 18 q^{3} - 50 q^{5} - 4240 q^{9} + O(q^{10})$$ $$100 q + 18 q^{3} - 50 q^{5} - 4240 q^{9} + 10 q^{11} + 792 q^{13} + 1372 q^{15} - 1698 q^{17} - 242 q^{19} + 7186 q^{23} - 30744 q^{25} - 16716 q^{27} - 9416 q^{29} + 5490 q^{31} - 1886 q^{33} + 11970 q^{37} - 5252 q^{39} + 22536 q^{41} - 3400 q^{43} - 2332 q^{45} - 9426 q^{47} - 77586 q^{51} - 4286 q^{53} + 34724 q^{55} - 82972 q^{57} + 16962 q^{59} - 11194 q^{61} - 46068 q^{65} + 37358 q^{67} + 73700 q^{69} + 323536 q^{71} + 18326 q^{73} + 154248 q^{75} - 89582 q^{79} - 600894 q^{81} - 247088 q^{83} + 103380 q^{85} - 15916 q^{87} - 184906 q^{89} + 197246 q^{93} + 282046 q^{95} + 385608 q^{97} - 572928 q^{99} + O(q^{100})$$

Decomposition of $$S_{6}^{\mathrm{new}}(392, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
392.6.i.a $2$ $62.870$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-30$$ $$-32$$ $$0$$ $$q+(-30+30\zeta_{6})q^{3}-2^{5}\zeta_{6}q^{5}-657\zeta_{6}q^{9}+\cdots$$
392.6.i.b $2$ $62.870$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-20$$ $$74$$ $$0$$ $$q+(-20+20\zeta_{6})q^{3}+74\zeta_{6}q^{5}-157\zeta_{6}q^{9}+\cdots$$
392.6.i.c $2$ $62.870$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-6$$ $$4$$ $$0$$ $$q+(-6+6\zeta_{6})q^{3}+4\zeta_{6}q^{5}+207\zeta_{6}q^{9}+\cdots$$
392.6.i.d $2$ $62.870$ $$\Q(\sqrt{-3})$$ None $$0$$ $$6$$ $$-4$$ $$0$$ $$q+(6-6\zeta_{6})q^{3}-4\zeta_{6}q^{5}+207\zeta_{6}q^{9}+\cdots$$
392.6.i.e $2$ $62.870$ $$\Q(\sqrt{-3})$$ None $$0$$ $$20$$ $$-74$$ $$0$$ $$q+(20-20\zeta_{6})q^{3}-74\zeta_{6}q^{5}-157\zeta_{6}q^{9}+\cdots$$
392.6.i.f $2$ $62.870$ $$\Q(\sqrt{-3})$$ None $$0$$ $$30$$ $$32$$ $$0$$ $$q+(30-30\zeta_{6})q^{3}+2^{5}\zeta_{6}q^{5}-657\zeta_{6}q^{9}+\cdots$$
392.6.i.g $4$ $62.870$ $$\Q(\sqrt{-3}, \sqrt{-59})$$ None $$0$$ $$-26$$ $$-62$$ $$0$$ $$q+(-13-13\beta _{1}+\beta _{3})q^{3}+(31\beta _{1}+5\beta _{2}+\cdots)q^{5}+\cdots$$
392.6.i.h $4$ $62.870$ $$\Q(\sqrt{-3}, \sqrt{193})$$ None $$0$$ $$-14$$ $$42$$ $$0$$ $$q+(-7\beta _{1}-\beta _{2})q^{3}+(21-21\beta _{1}-5\beta _{2}+\cdots)q^{5}+\cdots$$
392.6.i.i $4$ $62.870$ $$\Q(\sqrt{-3}, \sqrt{-115})$$ None $$0$$ $$-6$$ $$82$$ $$0$$ $$q+(3\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(41+41\beta _{1}+\cdots)q^{5}+\cdots$$
392.6.i.j $4$ $62.870$ $$\Q(\sqrt{-3}, \sqrt{-115})$$ None $$0$$ $$6$$ $$-82$$ $$0$$ $$q+(3+3\beta _{1}-\beta _{3})q^{3}+(41\beta _{1}-3\beta _{2}+\cdots)q^{5}+\cdots$$
392.6.i.k $4$ $62.870$ $$\Q(\sqrt{-3}, \sqrt{193})$$ None $$0$$ $$14$$ $$-42$$ $$0$$ $$q+(7\beta _{1}-\beta _{2})q^{3}+(-21+21\beta _{1}-5\beta _{2}+\cdots)q^{5}+\cdots$$
392.6.i.l $4$ $62.870$ $$\Q(\sqrt{-3}, \sqrt{-59})$$ None $$0$$ $$26$$ $$62$$ $$0$$ $$q+(-13\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(31+31\beta _{1}+\cdots)q^{5}+\cdots$$
392.6.i.m $8$ $62.870$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}+\beta _{6})q^{3}+(-2\beta _{2}+\beta _{3})q^{5}+\cdots$$
392.6.i.n $8$ $62.870$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}-\beta _{5}q^{5}+(23-23\beta _{3}-\beta _{4}+\cdots)q^{9}+\cdots$$
392.6.i.o $10$ $62.870$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$5$$ $$-81$$ $$0$$ $$q+(1-\beta _{1}+\beta _{3})q^{3}+(-\beta _{1}+\beta _{2}+2^{4}\beta _{3}+\cdots)q^{5}+\cdots$$
392.6.i.p $10$ $62.870$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$13$$ $$31$$ $$0$$ $$q+(3+3\beta _{1}-\beta _{4})q^{3}+(-6\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots$$
392.6.i.q $12$ $62.870$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{3}+(\beta _{4}-\beta _{5})q^{5}+(20+20\beta _{1}+\cdots)q^{9}+\cdots$$
392.6.i.r $16$ $62.870$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{5}+\beta _{8})q^{5}+(-116-117\beta _{2}+\cdots)q^{9}+\cdots$$

Decomposition of $$S_{6}^{\mathrm{old}}(392, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(392, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(196, [\chi])$$$$^{\oplus 2}$$