Space of modular forms of level 46, weight 4, and Character 46.c

• Label: 46.4.c
• Level: $46$
• Weight: $4$
• Character orbit: 46.c
• Rep. character: $\chi_{46}(3,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $60$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(46, [\chi])\).

	Total	New	Old
Modular forms	200	60	140
Cusp forms	160	60	100
Eisenstein series	40	0	40

Trace form

60 * q + 8 * q^3 - 24 * q^4 + 10 * q^5 + 8 * q^6 - 8 * q^7 - 146 * q^9 + 20 * q^10 + 34 * q^11 + 32 * q^12 + 112 * q^13 - 40 * q^14 + 744 * q^15 - 96 * q^16 + 148 * q^17 + 40 * q^18 - 258 * q^19 - 312 * q^20 - 1060 * q^21 - 296 * q^22 - 968 * q^23 + 32 * q^24 - 782 * q^25 - 412 * q^26 + 272 * q^27 + 144 * q^28 + 716 * q^29 + 1016 * q^30 + 1256 * q^31 + 988 * q^33 + 520 * q^34 + 886 * q^35 - 584 * q^36 + 894 * q^37 + 436 * q^38 + 312 * q^39 + 80 * q^40 - 1034 * q^41 + 64 * q^42 - 1350 * q^43 + 136 * q^44 - 2644 * q^45 - 92 * q^46 - 3256 * q^47 + 128 * q^48 - 1024 * q^49 - 728 * q^50 + 328 * q^51 + 448 * q^52 - 448 * q^53 + 3252 * q^54 + 5564 * q^55 + 1776 * q^56 + 9364 * q^57 + 1552 * q^58 + 3814 * q^59 + 72 * q^60 - 414 * q^61 - 868 * q^62 - 4600 * q^63 - 384 * q^64 - 6368 * q^65 - 5360 * q^66 - 3330 * q^67 - 3104 * q^68 - 7756 * q^69 - 5968 * q^70 - 5512 * q^71 - 1952 * q^72 - 1132 * q^73 - 3564 * q^74 + 4410 * q^75 - 152 * q^76 + 224 * q^77 + 812 * q^78 + 3178 * q^79 + 1568 * q^80 + 4126 * q^81 + 4000 * q^82 + 6808 * q^83 + 4824 * q^84 + 6262 * q^85 + 3856 * q^86 - 2090 * q^87 + 752 * q^88 - 826 * q^89 + 4804 * q^90 - 2048 * q^91 - 3804 * q^93 - 1008 * q^94 - 272 * q^95 + 128 * q^96 + 11758 * q^97 + 6120 * q^98 + 8964 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(46, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
46.4.c.a	$46$	$4$	46.c	23.c	$11$	$30$	$3$	$2.714$		None		✓			46.4.c.a	$2$	$0$	\(-6\)	\(6\)	\(10\)	\(107\)		$\mathrm{SU}(2)[C_{11}]$
46.4.c.b	$46$	$4$	46.c	23.c	$11$	$30$	$3$	$2.714$		None		✓			46.4.c.b	$2$	$0$	\(6\)	\(2\)	\(0\)	\(-115\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{4}^{\mathrm{old}}(46, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(46, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)