Space of modular forms of level 468, weight 2, and Character 468.cg

• Label: 468.2.cg
• Level: $468$
• Weight: $2$
• Character orbit: 468.cg
• Rep. character: $\chi_{468}(5,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.cg (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(468, [\chi])\).

	Total	New	Old
Modular forms	360	56	304
Cusp forms	312	56	256
Eisenstein series	48	0	48

Trace form

56 * q - 2 * q^7 - 12 * q^11 - 12 * q^15 + 4 * q^19 - 12 * q^21 + 36 * q^27 - 4 * q^31 + 12 * q^33 - 4 * q^37 + 24 * q^41 + 6 * q^45 + 66 * q^47 - 48 * q^57 - 30 * q^63 - 78 * q^65 - 14 * q^67 + 28 * q^73 - 24 * q^79 - 78 * q^83 + 36 * q^85 - 8 * q^91 + 6 * q^93 + 26 * q^97 + 54 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(468, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
468.2.cg.a	$468$	$2$	468.cg	117.z	$12$	$56$	$14$	$3.737$		None		✓	✓	✓	468.2.cg.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(468, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(468, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)