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

• Label: 294.2.p
• Level: $294$
• Weight: $2$
• Character orbit: 294.p
• Rep. character: $\chi_{294}(5,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $216$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.p (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	720	216	504
Cusp forms	624	216	408
Eisenstein series	96	0	96

Trace form

\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
294.2.p.a	$294$	$2$	294.p	147.o	$42$	$216$	$18$	$2.348$		None		✓	✓	✓	294.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{42}]$

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

\( S_{2}^{\mathrm{old}}(294, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)