Space of modular forms of level 93, weight 6, and trivial character

• Label: 93.6.a
• Level: $93$
• Weight: $6$
• Character orbit: 93.a
• Rep. character: $\chi_{93}(1,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	93.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(93))\).

	Total	New	Old
Modular forms	56	24	32
Cusp forms	52	24	28
Eisenstein series	4	0	4

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
\(+\)	\(+\)	\(+\)		\(13\)	\(7\)	\(6\)		\(12\)	\(7\)	\(5\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(14\)	\(5\)	\(9\)		\(13\)	\(5\)	\(8\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(15\)	\(8\)	\(7\)		\(14\)	\(8\)	\(6\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(14\)	\(4\)	\(10\)		\(13\)	\(4\)	\(9\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(27\)	\(11\)	\(16\)		\(25\)	\(11\)	\(14\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(29\)	\(13\)	\(16\)		\(27\)	\(13\)	\(14\)		\(2\)	\(0\)	\(2\)

Trace form

24 * q + 12 * q^2 + 396 * q^4 - 12 * q^5 + 40 * q^7 - 90 * q^8 + 1944 * q^9 - 1058 * q^10 + 1484 * q^11 + 792 * q^12 - 492 * q^13 + 978 * q^14 + 396 * q^15 + 7732 * q^16 - 5376 * q^17 + 972 * q^18 + 2312 * q^19 - 1662 * q^20 - 6868 * q^22 + 5716 * q^23 - 108 * q^24 + 21716 * q^25 - 19772 * q^26 + 4206 * q^28 - 13956 * q^29 - 4104 * q^30 - 5766 * q^31 - 2008 * q^32 - 2880 * q^33 + 33772 * q^34 + 6328 * q^35 + 32076 * q^36 + 8860 * q^37 + 21074 * q^38 - 12168 * q^39 - 63564 * q^40 - 5540 * q^41 + 20160 * q^42 - 46212 * q^43 - 26336 * q^44 - 972 * q^45 - 18280 * q^46 - 8080 * q^47 + 52704 * q^48 + 75268 * q^49 - 49286 * q^50 - 31248 * q^51 + 10984 * q^52 - 37448 * q^53 + 2044 * q^55 + 185936 * q^56 - 14328 * q^57 - 7248 * q^58 - 66440 * q^59 + 64260 * q^60 + 19256 * q^61 + 3240 * q^63 + 114530 * q^64 + 31404 * q^65 - 100080 * q^66 + 54096 * q^67 - 240356 * q^68 - 7200 * q^69 + 53682 * q^70 - 235520 * q^71 - 7290 * q^72 + 1276 * q^73 - 109744 * q^74 + 163800 * q^75 + 227370 * q^76 - 295396 * q^77 + 95076 * q^78 + 87232 * q^79 - 489582 * q^80 + 157464 * q^81 - 283730 * q^82 - 5048 * q^83 + 147384 * q^84 + 138696 * q^85 + 37748 * q^86 + 89928 * q^87 - 151476 * q^88 + 356824 * q^89 - 85698 * q^90 - 140684 * q^91 + 176548 * q^92 - 17298 * q^93 + 325964 * q^94 - 284632 * q^95 + 95724 * q^96 - 205236 * q^97 - 855878 * q^98 + 120204 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(93))\) 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
93.6.a.a	$93$	$6$	93.a	1.a	$1$	$4$	$4$	$14.916$	4.4.3911701.1	None	✓	✓	✓	✓	93.6.a.a	$1$	$1$	\(-3\)	\(36\)	\(-42\)	\(-284\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{2})q^{2}+9q^{3}+(13-4\beta _{1}+\cdots)q^{4}+\cdots\)
93.6.a.b	$93$	$6$	93.a	1.a	$1$	$5$	$5$	$14.916$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓	✓	93.6.a.b	$1$	$0$	\(9\)	\(-45\)	\(36\)	\(108\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{2}-9q^{3}+(11+\beta _{2}-\beta _{4})q^{4}+\cdots\)
93.6.a.c	$93$	$6$	93.a	1.a	$1$	$7$	$7$	$14.916$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	93.6.a.c	$1$	$1$	\(-3\)	\(-63\)	\(-64\)	\(-88\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-9q^{3}+(14+\beta _{2})q^{4}+(-9+\cdots)q^{5}+\cdots\)
93.6.a.d	$93$	$6$	93.a	1.a	$1$	$8$	$8$	$14.916$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓	✓	93.6.a.d	$1$	$0$	\(9\)	\(72\)	\(58\)	\(304\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+9q^{3}+(24+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(93))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(93)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)