Space of modular forms of level 92, weight 4, and trivial character

• Label: 92.4.a
• Level: $92$
• Weight: $4$
• Character orbit: 92.a
• Rep. character: $\chi_{92}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	92.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(92))\).

	Total	New	Old
Modular forms	39	6	33
Cusp forms	33	6	27
Eisenstein series	6	0	6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(23\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(13\)	\(0\)	\(13\)		\(11\)	\(0\)	\(11\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(7\)	\(0\)	\(7\)		\(5\)	\(0\)	\(5\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(11\)	\(3\)	\(8\)		\(10\)	\(3\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(8\)	\(3\)	\(5\)		\(7\)	\(3\)	\(4\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(21\)	\(3\)	\(18\)		\(18\)	\(3\)	\(15\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(18\)	\(3\)	\(15\)		\(15\)	\(3\)	\(12\)		\(3\)	\(0\)	\(3\)

Trace form

6 * q + 4 * q^3 - 10 * q^5 - 4 * q^7 + 50 * q^9 - 58 * q^11 + 56 * q^13 - 128 * q^15 - 116 * q^17 + 26 * q^19 + 100 * q^21 + 78 * q^25 + 424 * q^27 + 180 * q^29 - 216 * q^31 - 300 * q^33 - 80 * q^35 - 186 * q^37 + 288 * q^39 + 4 * q^41 - 498 * q^43 - 158 * q^45 - 424 * q^47 + 526 * q^49 + 8 * q^51 + 234 * q^53 - 224 * q^55 - 16 * q^57 + 776 * q^59 - 714 * q^61 + 2052 * q^63 - 672 * q^65 - 1566 * q^67 + 276 * q^69 + 1248 * q^71 + 124 * q^73 + 236 * q^75 - 1272 * q^77 + 820 * q^79 + 1094 * q^81 - 950 * q^83 - 284 * q^85 + 176 * q^87 - 276 * q^89 + 696 * q^91 - 4044 * q^93 - 688 * q^95 + 2020 * q^97 - 4674 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(92))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	23
92.4.a.a	$92$	$4$	92.a	1.a	$1$	$3$	$3$	$5.428$	3.3.1229.1	None	✓	✓	✓	✓	92.4.a.a	$1$	$1$	\(0\)	\(-4\)	\(-10\)	\(-46\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-4-\beta _{1}+3\beta _{2})q^{5}+\cdots\)
92.4.a.b	$92$	$4$	92.a	1.a	$1$	$3$	$3$	$5.428$	3.3.28669.1	None	✓	✓	✓	✓	92.4.a.b	$1$	$0$	\(0\)	\(8\)	\(0\)	\(42\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(3+\beta _{2})q^{3}+\beta _{1}q^{5}+(14-\beta _{1})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(92))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(92)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)