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

• Label: 234.2.f
• Level: $234$
• Weight: $2$
• Character orbit: 234.f
• Rep. character: $\chi_{234}(133,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $84$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(84\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	92	28	64
Cusp forms	76	28	48
Eisenstein series	16	0	16

Trace form

28 * q + 28 * q^4 - 4 * q^7 + 4 * q^9 - 16 * q^11 - 2 * q^13 - 8 * q^14 - 4 * q^15 + 28 * q^16 - 8 * q^17 + 8 * q^18 + 2 * q^19 + 20 * q^21 - 4 * q^23 - 14 * q^25 + 4 * q^26 - 18 * q^27 - 4 * q^28 + 20 * q^29 - 8 * q^30 + 2 * q^31 - 40 * q^33 - 12 * q^35 + 4 * q^36 + 2 * q^37 - 18 * q^38 + 18 * q^39 - 8 * q^41 + 10 * q^42 + 2 * q^43 - 16 * q^44 - 38 * q^45 - 40 * q^47 - 18 * q^49 - 4 * q^50 - 16 * q^51 - 2 * q^52 - 8 * q^53 - 8 * q^56 - 22 * q^57 - 32 * q^59 - 4 * q^60 + 14 * q^61 - 16 * q^62 + 12 * q^63 + 28 * q^64 + 56 * q^65 - 32 * q^66 + 14 * q^67 - 8 * q^68 + 30 * q^69 - 12 * q^71 + 8 * q^72 - 28 * q^73 - 18 * q^74 - 110 * q^75 + 2 * q^76 - 4 * q^77 - 42 * q^78 - 10 * q^79 + 52 * q^81 + 12 * q^82 + 42 * q^83 + 20 * q^84 - 8 * q^86 + 30 * q^87 + 4 * q^89 - 10 * q^90 - 4 * q^91 - 4 * q^92 + 66 * q^93 + 64 * q^95 - 22 * q^97 + 24 * q^98 + 10 * 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.f.a	$234$	$2$	234.f	117.h	$3$	$2$	$1$	$1.868$	\(\Q(\sqrt{-3}) \)	None		✓			234.2.f.a	$2$	$0$	\(-2\)	\(0\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
234.2.f.b	$234$	$2$	234.f	117.h	$3$	$2$	$1$	$1.868$	\(\Q(\sqrt{-3}) \)	None		✓			234.2.f.b	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-1+2\zeta_{6})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
234.2.f.c	$234$	$2$	234.f	117.h	$3$	$12$	$6$	$1.868$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			234.2.f.c	$2$	$0$	\(-12\)	\(0\)	\(-3\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-\beta _{3}-\beta _{6})q^{3}+q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
234.2.f.d	$234$	$2$	234.f	117.h	$3$	$12$	$6$	$1.868$	12.0.\(\cdots\).1	None		✓			234.2.f.d	$2$	$0$	\(12\)	\(0\)	\(1\)	\(-5\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(\beta _{9}+\beta _{10})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)

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

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