Space of modular forms of level 46, weight 5, and Character 46.d

• Label: 46.5.d
• Level: $46$
• Weight: $5$
• Character orbit: 46.d
• Rep. character: $\chi_{46}(5,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	46.d (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(46, [\chi])\).

	Total	New	Old
Modular forms	260	80	180
Cusp forms	220	80	140
Eisenstein series	40	0	40

Trace form

80 * q - 20 * q^3 - 64 * q^4 + 64 * q^6 - 108 * q^9 - 160 * q^12 - 4 * q^13 - 2926 * q^15 - 512 * q^16 + 990 * q^17 + 3392 * q^18 + 1914 * q^19 + 1584 * q^20 + 2706 * q^21 - 1284 * q^23 + 512 * q^24 - 4044 * q^25 - 2976 * q^26 - 10406 * q^27 - 2640 * q^28 + 1650 * q^29 + 1408 * q^30 + 5630 * q^31 + 13310 * q^33 - 8232 * q^35 - 864 * q^36 + 3520 * q^37 + 4332 * q^39 + 2316 * q^41 + 7216 * q^43 + 2912 * q^46 + 1692 * q^47 - 1280 * q^48 - 26872 * q^49 - 576 * q^50 - 17424 * q^51 - 32 * q^52 - 7392 * q^53 - 23712 * q^54 - 30884 * q^55 - 8448 * q^56 + 10758 * q^57 + 8640 * q^58 + 25920 * q^59 + 9856 * q^60 + 44968 * q^61 + 28512 * q^62 + 55550 * q^63 - 4096 * q^64 + 55902 * q^65 + 22528 * q^66 + 5852 * q^67 - 15554 * q^69 - 7424 * q^70 - 59718 * q^71 - 23552 * q^72 - 20288 * q^73 - 59136 * q^74 - 112514 * q^75 - 52206 * q^77 - 21728 * q^78 - 32120 * q^79 - 4224 * q^80 + 67176 * q^81 - 832 * q^82 + 76362 * q^83 + 30976 * q^84 + 73964 * q^85 + 60192 * q^86 + 34220 * q^87 + 7656 * q^89 + 5568 * q^92 + 61484 * q^93 - 30848 * q^94 - 142614 * q^95 + 4096 * q^96 - 127446 * q^97 - 36096 * q^98 - 115302 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(46, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
46.5.d.a	$46$	$5$	46.d	23.d	$22$	$80$	$8$	$4.755$		None		✓	✓	✓	46.5.d.a	$2$	$0$	\(0\)	\(-20\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{5}^{\mathrm{old}}(46, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(46, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)