Space of modular forms of level 234, weight 3, and Character 234.i

• Label: 234.3.i
• Level: $234$
• Weight: $3$
• Character orbit: 234.i
• Rep. character: $\chi_{234}(73,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $26$
• Newform subspaces: $5$
• Sturm bound: $126$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	234.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(126\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(234, [\chi])\).

	Total	New	Old
Modular forms	184	26	158
Cusp forms	152	26	126
Eisenstein series	32	0	32

Trace form

26 * q + 2 * q^2 - 6 * q^5 + 4 * q^7 - 4 * q^8 - 36 * q^11 + 8 * q^14 - 104 * q^16 - 44 * q^19 + 12 * q^20 + 24 * q^22 - 26 * q^26 + 8 * q^28 + 192 * q^29 + 116 * q^31 - 8 * q^32 + 12 * q^34 + 72 * q^35 + 98 * q^37 + 24 * q^40 - 114 * q^41 - 72 * q^44 - 144 * q^46 + 132 * q^47 - 178 * q^50 - 52 * q^52 - 324 * q^53 - 360 * q^55 - 24 * q^58 + 180 * q^59 + 108 * q^61 - 162 * q^65 + 100 * q^67 - 24 * q^68 + 168 * q^70 + 396 * q^71 + 226 * q^73 - 44 * q^74 + 88 * q^76 + 552 * q^79 + 24 * q^80 - 228 * q^83 - 612 * q^85 + 120 * q^86 + 174 * q^89 + 388 * q^91 - 288 * q^92 + 168 * q^94 - 574 * q^97 + 590 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(234, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
234.3.i.a	$234$	$3$	234.i	13.d	$4$	$2$	$1$	$6.376$	\(\Q(\sqrt{-1}) \)	None					26.3.d.a	$2$	$0$	\(-2\)	\(0\)	\(6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}+2 i q^{4}+(3 i+3)q^{5}+\cdots\)
234.3.i.b	$234$	$3$	234.i	13.d	$4$	$4$	$2$	$6.376$	\(\Q(\zeta_{12})\)	None					78.3.f.a	$2$	$0$	\(-4\)	\(0\)	\(-12\)	\(-4\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta_1-1)q^{2}+2\beta_1 q^{4}+(\beta_{2}-3\beta_1-3)q^{5}+\cdots\)
234.3.i.c	$234$	$3$	234.i	13.d	$4$	$6$	$3$	$6.376$	6.0.353139264.2	None		✓			234.3.i.c	$2$	$0$	\(-6\)	\(0\)	\(6\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
234.3.i.d	$234$	$3$	234.i	13.d	$4$	$6$	$3$	$6.376$	6.0.353139264.2	None		✓			234.3.i.c	$2$	$0$	\(6\)	\(0\)	\(-6\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
234.3.i.e	$234$	$3$	234.i	13.d	$4$	$8$	$4$	$6.376$	8.0.\(\cdots\).1	None			✓		78.3.f.b	$2$	$0$	\(8\)	\(0\)	\(0\)	\(4\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{3})q^{2}+2\beta _{3}q^{4}+\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(234, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(234, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)