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

• Label: 93.2.e
• Level: $93$
• Weight: $2$
• Character orbit: 93.e
• Rep. character: $\chi_{93}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $21$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
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	26	10	16
Cusp forms	18	10	8
Eisenstein series	8	0	8

Trace form

10 * q - q^3 + 4 * q^4 + 12 * q^8 - 5 * q^9 - 8 * q^10 + 2 * q^11 - 2 * q^12 - 5 * q^13 - 18 * q^14 + 16 * q^15 - 24 * q^16 - 6 * q^17 + 7 * q^19 - 18 * q^20 - 8 * q^21 + 16 * q^22 + 16 * q^23 - 6 * q^24 - 19 * q^25 - 2 * q^26 + 2 * q^27 - 4 * q^28 + 8 * q^31 - 16 * q^32 - 4 * q^33 + 12 * q^34 + 28 * q^35 - 2 * q^36 + q^37 + 14 * q^38 + 18 * q^39 + 4 * q^41 - 2 * q^42 - 5 * q^43 - 2 * q^44 - 4 * q^47 - 4 * q^48 - 13 * q^49 + 10 * q^50 + 10 * q^51 + 6 * q^52 + 10 * q^53 - 12 * q^55 + 8 * q^56 + 3 * q^57 + 32 * q^58 + 16 * q^59 + 36 * q^60 + 4 * q^61 + 12 * q^62 + 8 * q^64 - 6 * q^65 - 16 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 + 40 * q^70 - 32 * q^71 - 6 * q^72 - 5 * q^73 - 34 * q^74 - 15 * q^75 + 14 * q^76 - 76 * q^77 - 28 * q^78 - 16 * q^79 + 12 * q^80 - 5 * q^81 + 12 * q^82 + 28 * q^83 - 4 * q^84 + 8 * q^85 + 38 * q^86 - 8 * q^87 - 4 * q^88 - 20 * q^89 - 8 * q^90 + 56 * q^91 - 8 * q^92 - 23 * q^93 - 88 * q^94 - 52 * q^95 + 8 * q^96 - 46 * q^97 + 16 * q^98 + 2 * 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.e.a	$93$	$2$	93.e	31.c	$3$	$4$	$2$	$0.743$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			93.2.e.a	$2$	$0$	\(0\)	\(2\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
93.2.e.b	$93$	$2$	93.e	31.c	$3$	$6$	$3$	$0.743$	6.0.591408.1	None		✓	✓		93.2.e.b	$2$	$0$	\(0\)	\(-3\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)

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

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