Space of modular forms of level 11, weight 4, and trivial character

• Label: 11.4.a
• Level: $11$
• Weight: $4$
• Character orbit: 11.a
• Rep. character: $\chi_{11}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(11))\).

	Total	New	Old
Modular forms	4	2	2
Cusp forms	2	2	0
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(11\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(3\)	\(2\)	\(1\)		\(2\)	\(2\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(1\)	\(0\)	\(1\)		\(0\)	\(0\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

2 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 + 44 * q^9 + 50 * q^10 - 22 * q^11 - 40 * q^12 + 80 * q^13 - 4 * q^14 - 194 * q^15 - 8 * q^16 - 124 * q^17 + 92 * q^18 + 72 * q^19 + 88 * q^20 + 76 * q^21 - 22 * q^22 - 98 * q^23 + 252 * q^24 + 136 * q^25 - 40 * q^26 - 182 * q^27 - 128 * q^28 + 144 * q^29 - 266 * q^30 - 34 * q^31 - 104 * q^32 + 22 * q^33 - 52 * q^34 - 172 * q^35 - 80 * q^36 + 54 * q^37 + 432 * q^38 + 400 * q^39 - 492 * q^40 + 536 * q^41 - 140 * q^42 - 60 * q^43 + 88 * q^44 + 428 * q^45 - 314 * q^46 - 272 * q^47 + 776 * q^48 - 390 * q^49 + 232 * q^50 - 164 * q^51 - 560 * q^52 - 492 * q^53 - 110 * q^54 - 22 * q^55 + 120 * q^56 - 1512 * q^57 - 192 * q^58 + 634 * q^59 + 632 * q^60 + 840 * q^61 + 134 * q^62 + 248 * q^63 + 224 * q^64 - 880 * q^65 + 286 * q^66 + 754 * q^67 + 640 * q^68 + 962 * q^69 + 284 * q^70 - 678 * q^71 - 744 * q^72 - 400 * q^73 + 6 * q^74 - 520 * q^75 + 432 * q^76 - 220 * q^77 - 440 * q^78 + 316 * q^79 - 1544 * q^80 - 1294 * q^81 + 512 * q^82 + 468 * q^83 - 736 * q^84 + 452 * q^85 - 156 * q^86 + 1200 * q^87 + 132 * q^88 - 1842 * q^89 + 1532 * q^90 + 1280 * q^91 - 40 * q^92 - 638 * q^93 - 992 * q^94 + 2952 * q^95 - 952 * q^96 + 2194 * q^97 - 870 * q^98 - 484 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11
11.4.a.a	$11$	$4$	11.a	1.a	$1$	$2$	$2$	$0.649$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓	✓	11.4.a.a	$1$	$0$	\(2\)	\(-2\)	\(2\)	\(20\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(-1-4\beta )q^{3}+(-4+2\beta )q^{4}+\cdots\)