Space of modular forms of level 1, weight 16, and trivial character

• Label: 1.16.a
• Level: $1$
• Weight: $16$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $1$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	2	2	0
Cusp forms	1	1	0
Eisenstein series	1	1	0

Trace form

q + 216 * q^2 - 3348 * q^3 + 13888 * q^4 + 52110 * q^5 - 723168 * q^6 + 2822456 * q^7 - 4078080 * q^8 - 3139803 * q^9 + 11255760 * q^10 + 20586852 * q^11 - 46497024 * q^12 - 190073338 * q^13 + 609650496 * q^14 - 174464280 * q^15 - 1335947264 * q^16 + 1646527986 * q^17 - 678197448 * q^18 + 1563257180 * q^19 + 723703680 * q^20 - 9449582688 * q^21 + 4446760032 * q^22 + 9451116072 * q^23 + 13653411840 * q^24 - 27802126025 * q^25 - 41055841008 * q^26 + 58552201080 * q^27 + 39198268928 * q^28 - 36902568330 * q^29 - 37684284480 * q^30 + 71588483552 * q^31 - 154934083584 * q^32 - 68924780496 * q^33 + 355650044976 * q^34 + 147078182160 * q^35 - 43605584064 * q^36 - 1033652081554 * q^37 + 337663550880 * q^38 + 636365535624 * q^39 - 212508748800 * q^40 + 1641974018202 * q^41 - 2041109860608 * q^42 - 492403109308 * q^43 + 285910200576 * q^44 - 163615134330 * q^45 + 2041441071552 * q^46 - 3410684952624 * q^47 + 4472751439872 * q^48 + 3218696361993 * q^49 - 6005259221400 * q^50 - 5512575697128 * q^51 - 2639738518144 * q^52 + 6797151655902 * q^53 + 12647275433280 * q^54 + 1072780857720 * q^55 - 11510201364480 * q^56 - 5233785038640 * q^57 - 7970954759280 * q^58 + 9858856815540 * q^59 - 2422959920640 * q^60 + 4931842626902 * q^61 + 15463112447232 * q^62 - 8861955816168 * q^63 + 10310557892608 * q^64 - 9904721643180 * q^65 - 14887752587136 * q^66 - 28837826625364 * q^67 + 22866980669568 * q^68 - 31642336609056 * q^69 + 31768887346560 * q^70 + 125050114914552 * q^71 + 12804367818240 * q^72 - 82171455513478 * q^73 - 223268849615664 * q^74 + 93081517931700 * q^75 + 21710515715840 * q^76 + 58105483948512 * q^77 + 137454955694784 * q^78 - 25413078694480 * q^79 - 69616211927040 * q^80 - 150980027970519 * q^81 + 354666387931632 * q^82 - 281736730890468 * q^83 - 131235804370944 * q^84 + 85800573350460 * q^85 - 106359071610528 * q^86 + 123549798768840 * q^87 - 83954829404160 * q^88 + 715618564776810 * q^89 - 35340869015280 * q^90 - 536473633278128 * q^91 + 131257100007936 * q^92 - 239678242932096 * q^93 - 736707949766784 * q^94 + 81461331649800 * q^95 + 518719311839232 * q^96 + 612786136081826 * q^97 + 695238414190488 * q^98 - 64638659670156 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\) 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				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.16.a.a	$1$	$16$	1.a	1.a	$1$	$1$	$1$	$1.427$	\(\Q\)	None	✓	✓	✓	✓	1.16.a.a	$1$	$0$	\(216\)	\(-3348\)	\(52110\)	\(2822456\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+6^{3}q^{2}-3348q^{3}+13888q^{4}+52110q^{5}+\cdots\)