Space of modular forms of level 1218, weight 2, and Character 1218.i

• Label: 1218.2.i
• Level: $1218$
• Weight: $2$
• Character orbit: 1218.i
• Rep. character: $\chi_{1218}(697,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $9$
• Sturm bound: $480$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(480\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1218, [\chi])\).

	Total	New	Old
Modular forms	496	72	424
Cusp forms	464	72	392
Eisenstein series	32	0	32

Trace form

72 * q - 36 * q^4 + 8 * q^5 - 8 * q^7 - 36 * q^9 - 8 * q^10 + 16 * q^11 - 8 * q^14 - 36 * q^16 - 16 * q^17 + 8 * q^19 - 16 * q^20 - 8 * q^21 + 16 * q^22 + 8 * q^23 - 28 * q^25 + 8 * q^26 + 16 * q^28 - 8 * q^30 - 16 * q^31 + 72 * q^36 - 24 * q^37 - 8 * q^39 - 8 * q^40 - 16 * q^41 + 16 * q^43 + 16 * q^44 + 8 * q^45 + 8 * q^47 + 32 * q^49 + 16 * q^51 - 16 * q^55 + 16 * q^56 + 48 * q^57 - 16 * q^59 - 40 * q^61 - 48 * q^62 - 8 * q^63 + 72 * q^64 - 16 * q^66 - 32 * q^67 - 16 * q^68 + 16 * q^70 + 96 * q^71 + 8 * q^73 + 8 * q^74 + 16 * q^75 - 16 * q^76 + 64 * q^77 - 32 * q^78 + 16 * q^79 + 8 * q^80 - 36 * q^81 + 32 * q^82 - 64 * q^83 + 16 * q^84 + 32 * q^85 + 8 * q^86 - 8 * q^88 - 48 * q^89 + 16 * q^90 + 40 * q^91 - 16 * q^92 - 8 * q^93 + 24 * q^94 - 40 * q^95 - 96 * q^97 - 32 * q^98 - 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1218, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1218.2.i.a	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.64827.1	None		✓			1218.2.i.a	$2$	$0$	\(-3\)	\(-3\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{5})q^{2}-\beta _{5}q^{3}-\beta _{5}q^{4}+\beta _{1}q^{5}+\cdots\)
1218.2.i.b	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.1783323.2	None		✓			1218.2.i.b	$2$	$0$	\(-3\)	\(3\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots\)
1218.2.i.c	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.64827.1	None		✓			1218.2.i.c	$2$	$0$	\(3\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{2}+(-1+\beta _{5})q^{3}+(-1+\beta _{5})q^{4}+\cdots\)
1218.2.i.d	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.1783323.2	None		✓			1218.2.i.d	$2$	$0$	\(3\)	\(-3\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4})q^{2}-\beta _{4}q^{3}-\beta _{4}q^{4}+\beta _{1}q^{5}+\cdots\)
1218.2.i.e	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.18825075.4	None		✓			1218.2.i.e	$2$	$0$	\(3\)	\(-3\)	\(5\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{3})q^{2}+\beta _{3}q^{3}+\beta _{3}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
1218.2.i.f	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.1783323.2	None		✓			1218.2.i.f	$2$	$0$	\(3\)	\(3\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4})q^{2}+\beta _{4}q^{3}-\beta _{4}q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
1218.2.i.g	$1218$	$2$	1218.i	7.c	$3$	$12$	$6$	$9.726$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1218.2.i.g	$2$	$0$	\(-6\)	\(-6\)	\(-3\)	\(0\)	$3^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{8}q^{2}+(-1+\beta _{8})q^{3}+(-1+\beta _{8}+\cdots)q^{4}+\cdots\)
1218.2.i.h	$1218$	$2$	1218.i	7.c	$3$	$12$	$6$	$9.726$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1218.2.i.h	$2$	$0$	\(-6\)	\(6\)	\(3\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots\)
1218.2.i.i	$1218$	$2$	1218.i	7.c	$3$	$12$	$6$	$9.726$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1218.2.i.i	$2$	$0$	\(6\)	\(6\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{6}q^{2}+(1-\beta _{6})q^{3}+(-1+\beta _{6})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1218, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1218, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(203, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(406, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(609, [\chi])\)\(^{\oplus 2}\)