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

• Label: 294.2.f
• Level: $294$
• Weight: $2$
• Character orbit: 294.f
• Rep. character: $\chi_{294}(215,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $3$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.f (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(112\)
Trace bound:			\(1\)
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	28	116
Cusp forms	80	28	52
Eisenstein series	64	0	64

Trace form

28 * q + 14 * q^4 + 10 * q^9 + 6 * q^10 - 12 * q^15 - 14 * q^16 + 4 * q^18 - 12 * q^19 - 20 * q^22 - 6 * q^24 - 24 * q^25 - 4 * q^30 + 6 * q^31 + 18 * q^33 + 20 * q^36 + 28 * q^37 - 4 * q^39 + 6 * q^40 - 32 * q^43 + 12 * q^46 - 12 * q^51 - 12 * q^52 - 18 * q^54 - 8 * q^57 - 2 * q^58 - 6 * q^60 - 28 * q^64 - 20 * q^67 - 4 * q^72 - 24 * q^73 + 32 * q^78 - 54 * q^79 + 18 * q^81 + 24 * q^82 + 72 * q^85 + 18 * q^87 - 10 * q^88 + 24 * q^94 - 6 * q^96 - 112 * q^99

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.f.a	$294$	$2$	294.f	21.g	$6$	$4$	$2$	$2.348$	\(\Q(\zeta_{12})\)	None					42.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
294.2.f.b	$294$	$2$	294.f	21.g	$6$	$8$	$4$	$2.348$	\(\Q(\zeta_{24})\)	None					42.2.d.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{4}-\beta_1)q^{2}-\beta_{6} q^{3}+(-\beta_{2}+1)q^{4}+\cdots\)
294.2.f.c	$294$	$2$	294.f	21.g	$6$	$16$	$8$	$2.348$	\(\Q(\zeta_{48})\)	None		✓	✓		294.2.d.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{48}^{4}-\zeta_{48}^{12})q^{2}+(\zeta_{48}+\zeta_{48}^{3}+\cdots)q^{3}+\cdots\)

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

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