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

• Label: 234.2.x
• Level: $234$
• Weight: $2$
• Character orbit: 234.x
• Rep. character: $\chi_{234}(71,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $84$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	200	24	176
Cusp forms	136	24	112
Eisenstein series	64	0	64

Trace form

\( 24 q + 12 q^{10} + 36 q^{13} + 12 q^{16} - 48 q^{31} - 36 q^{34} - 36 q^{37} - 48 q^{43} - 48 q^{46} - 48 q^{49} + 48 q^{55} - 12 q^{58} + 36 q^{61} - 60 q^{73} + 96 q^{82} - 96 q^{85} + 48 q^{91} + 108 q^{97}+O(q^{100}) \)

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.x.a	$234$	$2$	234.x	39.k	$12$	$8$	$2$	$1.868$	\(\Q(\zeta_{24})\)	None		✓			234.2.x.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
234.2.x.b	$234$	$2$	234.x	39.k	$12$	$16$	$4$	$1.868$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		234.2.x.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{6}$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{3}q^{2}+\beta _{4}q^{4}+\beta _{14}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(234, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)