Space of modular forms of level 123, weight 4, and Character 123.i

• Label: 123.4.i
• Level: $123$
• Weight: $4$
• Character orbit: 123.i
• Rep. character: $\chi_{123}(14,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $160$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	123.i (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 123 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(123, [\chi])\).

	Total	New	Old
Modular forms	176	176	0
Cusp forms	160	160	0
Eisenstein series	16	16	0

Trace form

160 * q - 8 * q^3 + 56 * q^6 - 8 * q^7 - 16 * q^10 + 260 * q^12 + 136 * q^13 - 172 * q^15 - 2192 * q^16 - 8 * q^18 - 8 * q^19 + 580 * q^21 - 368 * q^22 - 420 * q^24 - 608 * q^27 + 504 * q^28 + 448 * q^30 + 1736 * q^33 - 728 * q^34 - 624 * q^36 - 112 * q^37 - 612 * q^39 - 664 * q^42 - 8 * q^43 - 96 * q^46 + 552 * q^48 + 1576 * q^49 + 2832 * q^51 + 2040 * q^52 - 772 * q^54 + 1672 * q^55 + 2456 * q^57 + 856 * q^58 - 3052 * q^60 + 1672 * q^61 + 3260 * q^63 + 3520 * q^67 + 256 * q^69 + 6632 * q^70 + 232 * q^73 - 2304 * q^75 - 8184 * q^76 + 2960 * q^78 - 2120 * q^79 + 1624 * q^82 - 5612 * q^84 - 11048 * q^85 - 7060 * q^87 - 7344 * q^88 - 5412 * q^90 - 10568 * q^91 - 2328 * q^93 + 20176 * q^94 + 36 * q^96 + 5608 * q^97 - 5704 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(123, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
123.4.i.a	$123$	$4$	123.i	123.i	$8$	$160$	$40$	$7.257$		None		✓	✓	✓	123.4.i.a	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{8}]$