Space of modular forms of level 92, weight 9, and Character 92.c

• Label: 92.9.c
• Level: $92$
• Weight: $9$
• Character orbit: 92.c
• Rep. character: $\chi_{92}(47,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	92.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(92, [\chi])\).

	Total	New	Old
Modular forms	98	88	10
Cusp forms	94	88	6
Eisenstein series	4	0	4

Trace form

88 * q - 336 * q^5 + 1617 * q^6 - 13707 * q^8 - 196264 * q^9 + 40114 * q^10 - 82415 * q^12 + 22832 * q^13 + 55992 * q^14 + 139024 * q^16 - 165648 * q^17 - 137887 * q^18 + 826404 * q^20 + 243648 * q^21 + 190556 * q^22 + 806812 * q^24 + 5352264 * q^25 - 400071 * q^26 - 144030 * q^28 - 68880 * q^29 + 4238350 * q^30 - 677400 * q^32 - 7361920 * q^33 + 3050514 * q^34 - 3205341 * q^36 + 7315760 * q^37 + 1382580 * q^38 + 10970414 * q^40 - 12346320 * q^41 + 7494600 * q^42 + 17441382 * q^44 + 3674160 * q^45 + 14005507 * q^48 - 91440872 * q^49 - 2588880 * q^50 + 8768159 * q^52 + 14065392 * q^53 + 31363867 * q^54 + 10203234 * q^56 + 11957760 * q^57 - 21193149 * q^58 - 49409940 * q^60 - 31411920 * q^61 - 78422451 * q^62 - 116044989 * q^64 - 10826592 * q^65 + 72565110 * q^66 - 44104524 * q^68 + 20281836 * q^70 - 16769577 * q^72 + 132336752 * q^73 - 105133362 * q^74 - 79234096 * q^76 - 38629440 * q^77 - 248872373 * q^78 + 467348814 * q^80 + 559801880 * q^81 + 99388093 * q^82 - 297509602 * q^84 - 101508064 * q^85 - 284552958 * q^86 - 36574500 * q^88 + 255434928 * q^89 + 159386596 * q^90 + 103559424 * q^93 + 453990485 * q^94 + 9030819 * q^96 - 182327632 * q^97 - 53187756 * q^98

Decomposition of \(S_{9}^{\mathrm{new}}(92, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
92.9.c.a	$92$	$9$	92.c	4.b	$2$	$88$	$88$	$37.479$		None		✓	✓	✓	92.9.c.a	$2$	$0$	\(0\)	\(0\)	\(-336\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{9}^{\mathrm{old}}(92, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(92, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)