Space of modular forms of level 92, weight 5, and Character 92.f

• Label: 92.5.f
• Level: $92$
• Weight: $5$
• Character orbit: 92.f
• Rep. character: $\chi_{92}(5,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.f (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(92, [\chi])\).

	Total	New	Old
Modular forms	510	80	430
Cusp forms	450	80	370
Eisenstein series	60	0	60

Trace form

80 * q + 10 * q^3 - 318 * q^9 + 2 * q^13 + 1463 * q^15 - 495 * q^17 - 957 * q^19 - 1353 * q^21 + 1614 * q^23 + 1890 * q^25 + 4723 * q^27 - 1617 * q^29 - 3271 * q^31 - 6655 * q^33 - 5280 * q^35 + 3520 * q^37 + 6138 * q^39 + 11370 * q^41 + 7216 * q^43 - 270 * q^47 - 14512 * q^49 - 17424 * q^51 - 7392 * q^53 + 5746 * q^55 + 18381 * q^57 + 11772 * q^59 - 22484 * q^61 - 27775 * q^63 - 27951 * q^65 - 2926 * q^67 + 15769 * q^69 + 19779 * q^71 + 24400 * q^73 + 2809 * q^75 + 19839 * q^77 + 21604 * q^79 + 22224 * q^81 - 11253 * q^83 - 25594 * q^85 + 45506 * q^87 + 7656 * q^89 + 7970 * q^93 - 22437 * q^95 + 32439 * q^97 - 48477 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(92, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
92.5.f.a	$92$	$5$	92.f	23.d	$22$	$80$	$8$	$9.510$		None		✓	✓	✓	92.5.f.a	$2$	$0$	\(0\)	\(10\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{5}^{\mathrm{old}}(92, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(92, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)