Space of modular forms of level 46, weight 11, and Character 46.b

• Label: 46.11.b
• Level: $46$
• Weight: $11$
• Character orbit: 46.b
• Rep. character: $\chi_{46}(45,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $66$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	46.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(66\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(46, [\chi])\).

	Total	New	Old
Modular forms	62	20	42
Cusp forms	58	20	38
Eisenstein series	4	0	4

Trace form

20 * q - 124 * q^3 + 10240 * q^4 - 12160 * q^6 + 362880 * q^9 - 63488 * q^12 + 1231780 * q^13 + 5242880 * q^16 + 6493952 * q^18 + 2731876 * q^23 - 6225920 * q^24 - 47471412 * q^25 - 13969408 * q^26 - 60370732 * q^27 + 13983036 * q^29 - 114197540 * q^31 - 3674824 * q^35 + 185794560 * q^36 + 212782668 * q^39 + 187451804 * q^41 - 153254528 * q^46 - 176842036 * q^47 - 32505856 * q^48 - 301556036 * q^49 - 498813184 * q^50 + 630671360 * q^52 - 1049943680 * q^54 - 980698936 * q^55 - 2124263680 * q^58 - 1996336600 * q^59 - 399937920 * q^62 + 2684354560 * q^64 + 5823216556 * q^69 - 875484672 * q^70 + 6504548036 * q^71 + 3324903424 * q^72 - 6299505740 * q^73 + 15103416188 * q^75 - 5739613672 * q^77 + 1920458624 * q^78 + 8435851172 * q^81 + 13542091008 * q^82 - 23104958520 * q^85 - 18763351196 * q^87 + 1398720512 * q^92 + 6244251196 * q^93 + 1725975680 * q^94 - 47659128608 * q^95 - 3187671040 * q^96 + 20634273536 * q^98

Decomposition of \(S_{11}^{\mathrm{new}}(46, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
46.11.b.a	$46$	$11$	46.b	23.b	$2$	$20$	$20$	$29.226$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	46.11.b.a	$2$	$0$	\(0\)	\(-124\)	\(0\)	\(0\)	$2^{62}\cdot 3^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-6+\beta _{1}+\beta _{3})q^{3}+2^{9}q^{4}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(46, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(46, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)