# Properties

 Label 294.6.e Level $294$ Weight $6$ Character orbit 294.e Rep. character $\chi_{294}(67,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $68$ Newform subspaces $26$ Sturm bound $336$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$294 = 2 \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 294.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$26$$ Sturm bound: $$336$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(294, [\chi])$$.

Total New Old
Modular forms 592 68 524
Cusp forms 528 68 460
Eisenstein series 64 0 64

## Trace form

 $$68 q - 544 q^{4} + 44 q^{5} + 144 q^{6} - 2754 q^{9} + O(q^{10})$$ $$68 q - 544 q^{4} + 44 q^{5} + 144 q^{6} - 2754 q^{9} - 648 q^{10} - 296 q^{11} + 3312 q^{13} + 396 q^{15} - 8704 q^{16} - 2612 q^{17} - 1020 q^{19} - 1408 q^{20} + 7120 q^{22} - 8652 q^{23} - 1152 q^{24} - 16568 q^{25} - 880 q^{26} - 29720 q^{29} + 8352 q^{30} + 18834 q^{31} - 6714 q^{33} + 12384 q^{34} + 88128 q^{36} + 43320 q^{37} - 816 q^{38} + 7344 q^{39} - 10368 q^{40} - 53424 q^{41} - 13808 q^{43} - 4736 q^{44} + 3564 q^{45} + 24080 q^{46} + 99492 q^{47} - 43904 q^{50} + 23328 q^{51} - 26496 q^{52} + 45556 q^{53} - 5832 q^{54} + 119028 q^{55} + 122256 q^{57} - 23560 q^{58} - 73096 q^{59} - 3168 q^{60} + 47592 q^{61} + 18080 q^{62} + 278528 q^{64} - 287620 q^{65} - 34848 q^{66} - 140164 q^{67} - 41792 q^{68} + 197784 q^{69} + 78808 q^{71} + 2544 q^{73} - 102704 q^{74} - 9432 q^{75} + 32640 q^{76} - 93312 q^{78} - 138962 q^{79} + 11264 q^{80} - 223074 q^{81} - 75264 q^{82} - 446624 q^{83} + 168872 q^{85} + 7664 q^{86} + 119574 q^{87} - 56960 q^{88} + 127008 q^{89} + 104976 q^{90} + 276864 q^{92} + 4824 q^{93} - 108192 q^{94} + 572036 q^{95} - 18432 q^{96} + 342372 q^{97} + 47952 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(294, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
294.6.e.a $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$-9$$ $$-66$$ $$0$$ $$q-4\zeta_{6}q^{2}+(-9+9\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.b $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$-9$$ $$-24$$ $$0$$ $$q-4\zeta_{6}q^{2}+(-9+9\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.c $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$-9$$ $$76$$ $$0$$ $$q-4\zeta_{6}q^{2}+(-9+9\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.d $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$9$$ $$-76$$ $$0$$ $$q-4\zeta_{6}q^{2}+(9-9\zeta_{6})q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+\cdots$$
294.6.e.e $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$9$$ $$-6$$ $$0$$ $$q-4\zeta_{6}q^{2}+(9-9\zeta_{6})q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+\cdots$$
294.6.e.f $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$9$$ $$24$$ $$0$$ $$q-4\zeta_{6}q^{2}+(9-9\zeta_{6})q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+\cdots$$
294.6.e.g $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$9$$ $$66$$ $$0$$ $$q-4\zeta_{6}q^{2}+(9-9\zeta_{6})q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+\cdots$$
294.6.e.h $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$-9$$ $$-54$$ $$0$$ $$q+4\zeta_{6}q^{2}+(-9+9\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.i $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$-9$$ $$-26$$ $$0$$ $$q+4\zeta_{6}q^{2}+(-9+9\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.j $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$-9$$ $$-26$$ $$0$$ $$q+4\zeta_{6}q^{2}+(-9+9\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.k $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$-9$$ $$44$$ $$0$$ $$q+4\zeta_{6}q^{2}+(-9+9\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.l $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$-9$$ $$72$$ $$0$$ $$q+4\zeta_{6}q^{2}+(-9+9\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.m $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$-9$$ $$86$$ $$0$$ $$q+4\zeta_{6}q^{2}+(-9+9\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.n $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$9$$ $$-72$$ $$0$$ $$q+4\zeta_{6}q^{2}+(9-9\zeta_{6})q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+\cdots$$
294.6.e.o $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$9$$ $$-44$$ $$0$$ $$q+4\zeta_{6}q^{2}+(9-9\zeta_{6})q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+\cdots$$
294.6.e.p $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$9$$ $$26$$ $$0$$ $$q+4\zeta_{6}q^{2}+(9-9\zeta_{6})q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+\cdots$$
294.6.e.q $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$9$$ $$26$$ $$0$$ $$q+4\zeta_{6}q^{2}+(9-9\zeta_{6})q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+\cdots$$
294.6.e.r $2$ $47.153$ $$\Q(\sqrt{-3})$$ None $$4$$ $$9$$ $$54$$ $$0$$ $$q+4\zeta_{6}q^{2}+(9-9\zeta_{6})q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+\cdots$$
294.6.e.s $4$ $47.153$ $$\Q(\sqrt{-3}, \sqrt{9601})$$ None $$-8$$ $$-18$$ $$-53$$ $$0$$ $$q-4\beta _{2}q^{2}+(-9+9\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.t $4$ $47.153$ $$\Q(\sqrt{-3}, \sqrt{4705})$$ None $$-8$$ $$-18$$ $$-18$$ $$0$$ $$q-4\beta _{1}q^{2}+(-9+9\beta _{1})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.u $4$ $47.153$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-8$$ $$-18$$ $$108$$ $$0$$ $$q+4\beta _{2}q^{2}+(-9-9\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
294.6.e.v $4$ $47.153$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-8$$ $$18$$ $$-108$$ $$0$$ $$q+4\beta _{2}q^{2}+(9+9\beta _{2})q^{3}+(-2^{4}-2^{4}\beta _{2}+\cdots)q^{4}+\cdots$$
294.6.e.w $4$ $47.153$ $$\Q(\sqrt{-3}, \sqrt{4705})$$ None $$-8$$ $$18$$ $$18$$ $$0$$ $$q-4\beta _{1}q^{2}+(9-9\beta _{1})q^{3}+(-2^{4}+2^{4}\beta _{1}+\cdots)q^{4}+\cdots$$
294.6.e.x $4$ $47.153$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$8$$ $$-18$$ $$-108$$ $$0$$ $$q+(4+4\beta _{2})q^{2}+9\beta _{2}q^{3}+2^{4}\beta _{2}q^{4}+\cdots$$
294.6.e.y $4$ $47.153$ $$\Q(\sqrt{-3}, \sqrt{505})$$ None $$8$$ $$18$$ $$17$$ $$0$$ $$q+4\beta _{1}q^{2}+(9-9\beta _{1})q^{3}+(-2^{4}+2^{4}\beta _{1}+\cdots)q^{4}+\cdots$$
294.6.e.z $4$ $47.153$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$8$$ $$18$$ $$108$$ $$0$$ $$q-4\beta _{2}q^{2}+(9+9\beta _{2})q^{3}+(-2^{4}-2^{4}\beta _{2}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(294, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(294, [\chi]) \simeq$$ $$S_{6}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 2}$$