Space of modular forms of level 294, weight 2, and Character 294.e

• Label: 294.2.e
• Level: $294$
• Weight: $2$
• Character orbit: 294.e
• Rep. character: $\chi_{294}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $6$
• Sturm bound: $112$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(112\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(294, [\chi])\).

	Total	New	Old
Modular forms	144	12	132
Cusp forms	80	12	68
Eisenstein series	64	0	64

Trace form

\( 12 q - 6 q^{4} + 4 q^{5} + 4 q^{6} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
294.2.e.a	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
294.2.e.b	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
294.2.e.c	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
294.2.e.d	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-1\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
294.2.e.e	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(1\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
294.2.e.f	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(1\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

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