Space of modular forms of level 234, weight 2, and Character 234.bd

• Label: 234.2.bd
• Level: $234$
• Weight: $2$
• Character orbit: 234.bd
• Rep. character: $\chi_{234}(5,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.bd (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(234, [\chi])\).

	Total	New	Old
Modular forms	184	56	128
Cusp forms	152	56	96
Eisenstein series	32	0	32

Trace form

56 * q + 4 * q^7 + 24 * q^11 - 24 * q^15 + 28 * q^16 - 8 * q^19 - 24 * q^21 - 36 * q^27 + 8 * q^28 - 4 * q^31 - 36 * q^33 + 8 * q^37 - 24 * q^39 - 48 * q^41 - 36 * q^42 + 60 * q^45 - 24 * q^47 - 24 * q^50 - 4 * q^52 - 36 * q^54 - 84 * q^63 + 48 * q^65 + 48 * q^66 + 28 * q^67 - 24 * q^72 - 56 * q^73 - 48 * q^74 + 4 * q^76 + 60 * q^78 + 48 * q^79 - 24 * q^83 - 24 * q^84 - 48 * q^86 - 96 * q^87 - 8 * q^91 + 48 * q^92 + 24 * q^93 + 20 * q^97 + 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(234, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
234.2.bd.a	$234$	$2$	234.bd	117.z	$12$	$56$	$14$	$1.868$		None		✓	✓	✓	234.2.bd.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(234, [\chi])\) into lower level spaces

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