Space of modular forms of level 93, weight 2, and trivial character

• Label: 93.2.a
• Level: $93$
• Weight: $2$
• Character orbit: 93.a
• Rep. character: $\chi_{93}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $2$
• Sturm bound: $21$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(21\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(93))\).

	Total	New	Old
Modular forms	12	5	7
Cusp forms	9	5	4
Eisenstein series	3	0	3

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

\(3\)	\(31\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(2\)	\(2\)	\(0\)		\(2\)	\(2\)	\(0\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(4\)	\(3\)	\(1\)		\(3\)	\(3\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(5\)	\(2\)	\(3\)		\(4\)	\(2\)	\(2\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(7\)	\(3\)	\(4\)		\(5\)	\(3\)	\(2\)		\(2\)	\(0\)	\(2\)

Trace form

5 * q - 3 * q^2 + q^3 + 5 * q^4 - 6 * q^5 + 3 * q^6 - 9 * q^8 + 5 * q^9 - 4 * q^10 - 8 * q^11 - q^12 + 2 * q^13 + 6 * q^14 + 2 * q^15 + 9 * q^16 - 6 * q^17 - 3 * q^18 - 4 * q^19 + 8 * q^21 + 8 * q^22 - 4 * q^23 + 3 * q^24 + 7 * q^25 + 2 * q^26 + q^27 - 26 * q^28 - 6 * q^29 - 6 * q^30 - 5 * q^31 - 11 * q^32 + 4 * q^33 + 6 * q^34 + 8 * q^35 + 5 * q^36 + 2 * q^37 + 34 * q^38 + 6 * q^39 - 6 * q^40 - 10 * q^41 - 16 * q^42 + 8 * q^43 - 4 * q^44 - 6 * q^45 - 24 * q^46 + 16 * q^47 - 17 * q^48 + q^49 + 29 * q^50 + 2 * q^51 + 6 * q^52 - 10 * q^53 + 3 * q^54 - 12 * q^55 + 28 * q^56 + 12 * q^57 - 2 * q^58 + 20 * q^59 - 18 * q^60 + 14 * q^61 + 3 * q^62 - 17 * q^64 - 24 * q^65 - 20 * q^66 - 12 * q^67 + 38 * q^68 - 8 * q^69 + 14 * q^70 + 8 * q^71 - 9 * q^72 - 10 * q^73 - 2 * q^74 - 9 * q^75 - 14 * q^76 + 4 * q^77 - 14 * q^78 + 16 * q^79 + 12 * q^80 + 5 * q^81 - 12 * q^82 - 4 * q^83 + 16 * q^84 + 4 * q^85 - 32 * q^86 - 10 * q^87 + 40 * q^88 - 22 * q^89 - 4 * q^90 + 4 * q^91 + 20 * q^92 - q^93 + 16 * q^94 + 16 * q^95 + 19 * q^96 + 22 * q^97 - 25 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(93))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	31
93.2.a.a	$93$	$2$	93.a	1.a	$1$	$2$	$2$	$0.743$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	93.2.a.a	$1$	$1$	\(-3\)	\(-2\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-3+\cdots)q^{5}+\cdots\)
93.2.a.b	$93$	$2$	93.a	1.a	$1$	$3$	$3$	$0.743$	3.3.229.1	None	✓	✓	✓	✓	93.2.a.b	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(93))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(93)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)