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

• Label: 234.2.b
• Level: $234$
• Weight: $2$
• Character orbit: 234.b
• Rep. character: $\chi_{234}(181,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $84$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(84\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	50	4	46
Cusp forms	34	4	30
Eisenstein series	16	0	16

Trace form

4 * q - 4 * q^4 + 2 * q^10 - 2 * q^13 + 2 * q^14 + 4 * q^16 - 2 * q^17 + 4 * q^23 - 6 * q^25 + 2 * q^26 + 20 * q^29 - 26 * q^35 - 24 * q^38 - 2 * q^40 + 6 * q^43 + 2 * q^49 + 2 * q^52 + 24 * q^53 - 2 * q^56 - 12 * q^61 + 20 * q^62 - 4 * q^64 - 26 * q^65 + 2 * q^68 + 22 * q^74 + 20 * q^79 - 20 * q^82 - 26 * q^91 - 4 * q^92 + 18 * q^94 + 12 * q^95

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.b.a	$234$	$2$	234.b	13.b	$2$	$2$	$2$	$1.868$	\(\Q(\sqrt{-1}) \)	None					78.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+2 i q^{5}+2 i q^{7}-i q^{8}+\cdots\)
234.2.b.b	$234$	$2$	234.b	13.b	$2$	$2$	$2$	$1.868$	\(\Q(\sqrt{-1}) \)	None					26.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-3 i q^{5}-3 i q^{7}-i q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(234, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)