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

• Label: 234.2.h
• Level: $234$
• Weight: $2$
• Character orbit: 234.h
• Rep. character: $\chi_{234}(55,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $5$
• Sturm bound: $84$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(84\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	100	14	86
Cusp forms	68	14	54
Eisenstein series	32	0	32

Trace form

14 * q - q^2 - 7 * q^4 - 2 * q^5 - 4 * q^7 + 2 * q^8 - q^10 + 12 * q^11 - 7 * q^13 - 8 * q^14 - 7 * q^16 + 5 * q^17 + 8 * q^19 + q^20 - 4 * q^22 - 4 * q^23 + 40 * q^25 + 3 * q^26 - 4 * q^28 - 7 * q^29 - 8 * q^31 - q^32 - 22 * q^34 + 4 * q^35 - 13 * q^37 + 2 * q^40 - 7 * q^41 - 16 * q^43 - 24 * q^44 - 12 * q^46 - 15 * q^49 - 4 * q^50 + 2 * q^52 + 14 * q^53 + 20 * q^55 + 4 * q^56 + 15 * q^58 - 12 * q^59 + 23 * q^61 + 12 * q^62 + 14 * q^64 + 33 * q^65 + 28 * q^67 + 5 * q^68 + 56 * q^70 - 16 * q^71 - 38 * q^73 + 21 * q^74 + 8 * q^76 - 48 * q^77 - 56 * q^79 + q^80 - q^82 + 29 * q^85 + 16 * q^86 - 4 * q^88 + 14 * q^89 - 88 * q^91 + 8 * q^92 - 16 * q^94 + 8 * q^95 + 2 * q^97 + 15 * q^98

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.h.a	$234$	$2$	234.h	13.c	$3$	$2$	$1$	$1.868$	\(\Q(\sqrt{-3}) \)	None					78.2.e.a	$2$	$0$	\(-1\)	\(0\)	\(-6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}-2\zeta_{6}q^{7}+\cdots\)
234.2.h.b	$234$	$2$	234.h	13.c	$3$	$2$	$1$	$1.868$	\(\Q(\sqrt{-3}) \)	None					78.2.e.b	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+2\zeta_{6}q^{7}+\cdots\)
234.2.h.c	$234$	$2$	234.h	13.c	$3$	$2$	$1$	$1.868$	\(\Q(\sqrt{-3}) \)	None					26.2.c.a	$2$	$0$	\(1\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-4\zeta_{6}q^{7}+\cdots\)
234.2.h.d	$234$	$2$	234.h	13.c	$3$	$4$	$2$	$1.868$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		✓			234.2.h.d	$2$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
234.2.h.e	$234$	$2$	234.h	13.c	$3$	$4$	$2$	$1.868$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		✓			234.2.h.d	$2$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+\cdots\)

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

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