# Properties

 Label 294.3.g Level $294$ Weight $3$ Character orbit 294.g Rep. character $\chi_{294}(19,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $28$ Newform subspaces $5$ Sturm bound $168$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$294 = 2 \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 294.g (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$168$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(294, [\chi])$$.

Total New Old
Modular forms 256 28 228
Cusp forms 192 28 164
Eisenstein series 64 0 64

## Trace form

 $$28q - 6q^{3} - 28q^{4} - 12q^{5} + 42q^{9} + O(q^{10})$$ $$28q - 6q^{3} - 28q^{4} - 12q^{5} + 42q^{9} + 24q^{10} + 12q^{11} + 12q^{12} - 24q^{15} - 56q^{16} + 48q^{17} + 42q^{19} + 16q^{22} - 32q^{23} + 66q^{25} - 96q^{26} - 80q^{29} + 48q^{30} - 102q^{31} + 36q^{33} - 168q^{36} - 26q^{37} - 24q^{38} - 90q^{39} - 48q^{40} + 412q^{43} + 24q^{44} - 36q^{45} + 96q^{46} + 132q^{47} + 32q^{50} + 72q^{51} - 12q^{52} - 48q^{53} - 516q^{57} - 176q^{58} + 24q^{59} + 24q^{60} + 72q^{61} + 224q^{64} + 228q^{65} + 286q^{67} - 96q^{68} - 440q^{71} + 66q^{73} - 384q^{74} - 66q^{75} - 288q^{78} - 426q^{79} + 48q^{80} - 126q^{81} - 48q^{82} + 1680q^{85} - 40q^{86} - 16q^{88} + 72q^{89} + 128q^{92} + 342q^{93} + 24q^{94} + 140q^{95} + 72q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(294, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
294.3.g.a $$4$$ $$8.011$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-6$$ $$-12$$ $$0$$ $$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$$
294.3.g.b $$4$$ $$8.011$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-6$$ $$12$$ $$0$$ $$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$$
294.3.g.c $$4$$ $$8.011$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$6$$ $$-12$$ $$0$$ $$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots$$
294.3.g.d $$8$$ $$8.011$$ 8.0.339738624.1 None $$0$$ $$-12$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{5})q^{2}+(-2-\beta _{4})q^{3}+2\beta _{4}q^{4}+\cdots$$
294.3.g.e $$8$$ $$8.011$$ 8.0.339738624.1 None $$0$$ $$12$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{5})q^{2}+(2+\beta _{4})q^{3}+2\beta _{4}q^{4}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(294, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(294, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 2}$$