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

• Label: 294.2.m
• Level: $294$
• Weight: $2$
• Character orbit: 294.m
• Rep. character: $\chi_{294}(25,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $120$
• Newform subspaces: $4$
• Sturm bound: $112$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.m (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(112\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	720	120	600
Cusp forms	624	120	504
Eisenstein series	96	0	96

Trace form

120 * q + 10 * q^4 + 4 * q^5 + 4 * q^6 - 6 * q^7 + 10 * q^9 - 2 * q^10 + 36 * q^11 + 8 * q^13 - 8 * q^14 + 10 * q^15 + 10 * q^16 + 24 * q^17 + 32 * q^19 + 20 * q^20 - 4 * q^21 + 2 * q^22 + 4 * q^23 - 2 * q^24 + 20 * q^25 + 32 * q^26 + 6 * q^28 - 24 * q^29 + 2 * q^31 - 2 * q^33 + 8 * q^34 + 36 * q^35 - 20 * q^36 + 36 * q^37 - 44 * q^38 - 32 * q^39 - 30 * q^40 - 112 * q^41 - 50 * q^42 - 8 * q^43 - 48 * q^44 - 52 * q^45 + 4 * q^46 - 40 * q^47 - 110 * q^49 - 16 * q^50 - 104 * q^51 - 4 * q^52 - 100 * q^53 - 2 * q^54 + 14 * q^55 - 52 * q^56 + 16 * q^57 - 36 * q^58 - 92 * q^59 - 26 * q^60 - 72 * q^61 - 64 * q^62 - 20 * q^64 + 28 * q^65 - 8 * q^66 + 8 * q^67 - 4 * q^68 - 8 * q^69 + 16 * q^70 - 40 * q^71 + 96 * q^73 + 40 * q^74 + 8 * q^75 - 8 * q^76 + 112 * q^77 + 40 * q^78 + 18 * q^79 + 4 * q^80 + 10 * q^81 + 4 * q^83 + 8 * q^84 - 16 * q^85 + 104 * q^86 + 28 * q^87 + 34 * q^88 - 28 * q^89 + 4 * q^90 - 64 * q^91 - 8 * q^92 + 28 * q^94 - 188 * q^95 - 2 * q^96 + 44 * q^97 - 24 * q^98 - 16 * 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.m.a	$294$	$2$	294.m	49.g	$21$	$24$	$2$	$2.348$		None		✓			294.2.m.a	$2$	$0$	\(-2\)	\(-2\)	\(1\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
294.2.m.b	$294$	$2$	294.m	49.g	$21$	$24$	$2$	$2.348$		None		✓			294.2.m.b	$2$	$0$	\(2\)	\(2\)	\(1\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
294.2.m.c	$294$	$2$	294.m	49.g	$21$	$36$	$3$	$2.348$		None		✓			294.2.m.c	$2$	$0$	\(-3\)	\(3\)	\(2\)	\(-5\)		$\mathrm{SU}(2)[C_{21}]$
294.2.m.d	$294$	$2$	294.m	49.g	$21$	$36$	$3$	$2.348$		None		✓			294.2.m.d	$2$	$0$	\(3\)	\(-3\)	\(0\)	\(-1\)		$\mathrm{SU}(2)[C_{21}]$

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

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