Space of modular forms of level 11, weight 3, and Character 11.d

• Label: 11.3.d
• Level: $11$
• Weight: $3$
• Character orbit: 11.d
• Rep. character: $\chi_{11}(2,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(11, [\chi])\).

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

Trace form

4 * q - 5 * q^2 - 9 * q^4 - 4 * q^5 + 15 * q^6 + 10 * q^7 + 15 * q^8 - 11 * q^9 + q^11 - 30 * q^12 - 20 * q^13 - 10 * q^14 + 19 * q^16 + 30 * q^18 + 25 * q^19 + 44 * q^20 - 35 * q^22 - 20 * q^23 + 5 * q^24 + 9 * q^25 - 10 * q^26 + 15 * q^27 - 60 * q^28 - 40 * q^29 - 80 * q^30 - 58 * q^31 + 65 * q^33 + 130 * q^34 + 80 * q^35 + 26 * q^36 + 90 * q^37 - 60 * q^38 + 50 * q^39 - 60 * q^40 - 80 * q^41 - 10 * q^42 + 24 * q^44 - 24 * q^45 + 30 * q^46 - 30 * q^47 - 40 * q^48 - 109 * q^49 - 45 * q^50 - 195 * q^51 + 110 * q^52 + 120 * q^53 - 76 * q^55 + 100 * q^56 + 45 * q^57 + 40 * q^58 + 23 * q^59 + 140 * q^60 + 10 * q^61 + 200 * q^62 + 90 * q^63 - 149 * q^64 + 90 * q^66 - 230 * q^67 - 260 * q^68 - 10 * q^69 - 40 * q^70 + 148 * q^71 - 95 * q^72 + 300 * q^73 - 270 * q^74 + 45 * q^75 - 200 * q^77 - 200 * q^78 + 70 * q^79 - 84 * q^80 - 116 * q^81 + 25 * q^82 + 225 * q^83 + 90 * q^84 + 260 * q^85 + 175 * q^86 + 55 * q^88 + 122 * q^89 - 20 * q^90 - 80 * q^91 + 40 * q^92 - 200 * q^93 + 120 * q^94 - 100 * q^95 + 340 * q^96 - 165 * q^97 + 31 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(11, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.3.d.a	$11$	$3$	11.d	11.d	$10$	$4$	$1$	$0.300$	\(\Q(\zeta_{10})\)	None		✓	✓	✓	11.3.d.a	$2$	$0$	\(-5\)	\(0\)	\(-4\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots\)