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

• Label: 294.2.i
• Level: $294$
• Weight: $2$
• Character orbit: 294.i
• Rep. character: $\chi_{294}(43,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $112$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.i (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(112\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	360	48	312
Cusp forms	312	48	264
Eisenstein series	48	0	48

Trace form

48 * q + 2 * q^3 - 8 * q^4 + 8 * q^5 + 2 * q^6 + 8 * q^7 - 8 * q^9 + 8 * q^10 - 12 * q^11 + 2 * q^12 + 8 * q^13 + 8 * q^14 - 10 * q^15 - 8 * q^16 - 12 * q^17 - 4 * q^19 - 20 * q^20 + 6 * q^21 - 2 * q^22 + 8 * q^23 + 2 * q^24 + 12 * q^25 - 20 * q^26 + 2 * q^27 + 8 * q^28 + 24 * q^29 + 32 * q^31 + 8 * q^33 + 16 * q^34 + 12 * q^35 - 8 * q^36 + 2 * q^37 - 4 * q^38 - 50 * q^39 - 6 * q^40 - 8 * q^41 - 22 * q^42 + 36 * q^43 - 12 * q^44 - 20 * q^45 + 8 * q^46 - 92 * q^47 - 12 * q^48 - 8 * q^49 + 16 * q^50 - 40 * q^51 - 6 * q^52 - 32 * q^53 + 2 * q^54 - 62 * q^55 - 20 * q^56 + 12 * q^57 - 30 * q^58 - 28 * q^59 - 10 * q^60 + 14 * q^61 + 4 * q^62 - 6 * q^63 - 8 * q^64 + 56 * q^65 + 8 * q^66 + 44 * q^67 + 16 * q^68 + 32 * q^69 + 26 * q^70 + 40 * q^71 - 20 * q^73 - 4 * q^74 + 30 * q^75 + 24 * q^76 - 4 * q^77 - 40 * q^78 + 64 * q^79 + 8 * q^80 - 8 * q^81 + 48 * q^82 - 52 * q^83 + 6 * q^84 + 16 * q^85 - 44 * q^86 + 14 * q^87 - 16 * q^88 - 44 * q^89 + 8 * q^90 + 20 * q^91 + 8 * q^92 + 28 * q^93 + 20 * q^94 - 40 * q^95 + 2 * q^96 - 112 * q^97 + 48 * 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.i.a	$294$	$2$	294.i	49.e	$7$	$6$	$1$	$2.348$	\(\Q(\zeta_{14})\)	None		✓			294.2.i.a	$2$	$0$	\(-1\)	\(-1\)	\(5\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-1+\zeta_{14}-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{2}+\cdots\)
294.2.i.b	$294$	$2$	294.i	49.e	$7$	$12$	$2$	$2.348$	12.0.\(\cdots\).1	None		✓			294.2.i.b	$2$	$0$	\(2\)	\(-2\)	\(1\)	\(0\)	$7$	$\mathrm{SU}(2)[C_{7}]$	\(q-\beta _{1}q^{2}+\beta _{9}q^{3}-\beta _{4}q^{4}+(-\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
294.2.i.c	$294$	$2$	294.i	49.e	$7$	$12$	$2$	$2.348$	12.0.\(\cdots\).1	None		✓			294.2.i.c	$2$	$0$	\(2\)	\(2\)	\(-1\)	\(0\)	$7$	$\mathrm{SU}(2)[C_{7}]$	\(q+(1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{9})q^{2}+\cdots\)
294.2.i.d	$294$	$2$	294.i	49.e	$7$	$18$	$3$	$2.348$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓	✓		294.2.i.d	$2$	$0$	\(-3\)	\(3\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q-\beta _{4}q^{2}+(1-\beta _{4}-\beta _{7}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)

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

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