Space of modular forms of level 93, weight 2, and Character 93.f

• Label: 93.2.f
• Level: $93$
• Weight: $2$
• Character orbit: 93.f
• Rep. character: $\chi_{93}(4,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $21$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.f (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(21\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(93, [\chi])\).

	Total	New	Old
Modular forms	48	24	24
Cusp forms	32	24	8
Eisenstein series	16	0	16

Trace form

24 * q - 2 * q^3 - 12 * q^4 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 6 * q^9 - 14 * q^10 + 6 * q^11 - 6 * q^12 - 6 * q^13 - 10 * q^14 - 8 * q^15 - 20 * q^16 + 8 * q^17 + 4 * q^19 + 8 * q^20 + 14 * q^21 + 16 * q^22 - 10 * q^23 + 2 * q^24 + 12 * q^25 - 4 * q^26 - 2 * q^27 - 4 * q^29 + 8 * q^30 + 4 * q^31 + 108 * q^32 - 6 * q^33 - 36 * q^35 + 28 * q^36 - 20 * q^37 - 54 * q^38 + 10 * q^39 - 34 * q^40 - 2 * q^41 + 2 * q^42 - 32 * q^43 - 40 * q^44 - 18 * q^46 - 24 * q^47 - 14 * q^48 + 12 * q^49 - 32 * q^50 - 10 * q^51 + 76 * q^52 - 4 * q^53 + 4 * q^54 + 92 * q^56 - 12 * q^57 + 2 * q^58 + 20 * q^59 - 14 * q^60 + 4 * q^61 + 34 * q^62 - 8 * q^63 - 10 * q^64 + 20 * q^65 + 4 * q^66 + 44 * q^67 - 24 * q^68 + 24 * q^69 + 82 * q^70 + 60 * q^71 - 6 * q^72 - 14 * q^73 + 68 * q^74 - 2 * q^75 + 4 * q^76 + 20 * q^77 - 8 * q^78 - 16 * q^79 - 118 * q^80 - 6 * q^81 + 26 * q^82 - 80 * q^83 - 12 * q^84 - 12 * q^85 - 20 * q^86 - 20 * q^87 - 40 * q^88 + 22 * q^89 - 14 * q^90 - 26 * q^91 - 68 * q^92 + 30 * q^93 - 20 * q^94 - 26 * q^95 - 12 * q^96 - 116 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(93, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
93.2.f.a	$93$	$2$	93.f	31.d	$5$	$8$	$2$	$0.743$	\(\Q(\zeta_{15})\)	None		✓			93.2.f.a	$2$	$0$	\(3\)	\(2\)	\(-6\)	\(9\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta_{3}-\beta_1+1)q^{2}+(\beta_{5}+\beta_{4}+\beta_{2}+1)q^{3}+\cdots\)
93.2.f.b	$93$	$2$	93.f	31.d	$5$	$16$	$4$	$0.743$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		93.2.f.b	$2$	$0$	\(-3\)	\(-4\)	\(6\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(-1-\beta _{8}-\beta _{9}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(93, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(93, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)