Space of modular forms of level 111, weight 2, and Character 111.e

• Label: 111.2.e
• Level: $111$
• Weight: $2$
• Character orbit: 111.e
• Rep. character: $\chi_{111}(10,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $25$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	111.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(25\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(111, [\chi])\).

	Total	New	Old
Modular forms	28	16	12
Cusp forms	20	16	4
Eisenstein series	8	0	8

Trace form

16 * q - 2 * q^3 - 10 * q^4 + 4 * q^5 - 2 * q^7 + 12 * q^8 - 8 * q^9 + 4 * q^10 - 16 * q^11 - 6 * q^12 - 4 * q^13 + 12 * q^14 - 14 * q^16 + 4 * q^17 - 2 * q^19 + 10 * q^20 + 2 * q^21 - 10 * q^22 - 12 * q^23 - 4 * q^25 + 16 * q^26 + 4 * q^27 - 8 * q^28 - 32 * q^29 - 8 * q^30 + 20 * q^31 - 2 * q^32 - 2 * q^33 + 8 * q^34 + 10 * q^35 + 20 * q^36 + 18 * q^37 + 28 * q^38 + 10 * q^39 - 32 * q^40 - 18 * q^41 - 16 * q^42 + 54 * q^44 - 8 * q^45 - 28 * q^46 - 20 * q^47 + 44 * q^48 - 22 * q^49 + 20 * q^50 - 12 * q^51 + 10 * q^52 - 14 * q^53 - 4 * q^55 - 76 * q^56 - 12 * q^57 + 28 * q^58 + 4 * q^59 + 28 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 32 * q^64 + 30 * q^65 - 32 * q^66 - 12 * q^67 - 56 * q^68 + 8 * q^69 - 8 * q^70 + 12 * q^71 - 6 * q^72 + 52 * q^73 + 30 * q^74 + 20 * q^75 + 44 * q^76 + 20 * q^77 + 18 * q^78 - 16 * q^80 - 8 * q^81 + 40 * q^82 + 8 * q^83 - 20 * q^84 + 24 * q^85 + 24 * q^86 - 6 * q^87 - 28 * q^88 + 26 * q^89 - 2 * q^90 + 12 * q^91 - 20 * q^92 + 22 * q^93 - 30 * q^94 - 22 * q^95 - 10 * q^96 + 4 * q^97 - 30 * q^98 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(111, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
111.2.e.a	$111$	$2$	111.e	37.c	$3$	$6$	$3$	$0.886$	6.0.1415907.1	None		✓			111.2.e.a	$2$	$0$	\(0\)	\(3\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(1+\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
111.2.e.b	$111$	$2$	111.e	37.c	$3$	$10$	$5$	$0.886$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		111.2.e.b	$2$	$0$	\(0\)	\(-5\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}+(-1+\beta _{6})q^{3}+(-2+2\beta _{6}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(111, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(111, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)