Space of modular forms of level 2, weight 16, and trivial character

• Label: 2.16.a
• Level: $2$
• Weight: $16$
• Character orbit: 2.a
• Rep. character: $\chi_{2}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	2.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 \(M_{16}(\Gamma_0(2))\).

	Total	New	Old
Modular forms	5	1	4
Cusp forms	3	1	2
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.

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

Trace form

q - 128 * q^2 + 6252 * q^3 + 16384 * q^4 + 90510 * q^5 - 800256 * q^6 + 56 * q^7 - 2097152 * q^8 + 24738597 * q^9 - 11585280 * q^10 - 95889948 * q^11 + 102432768 * q^12 - 59782138 * q^13 - 7168 * q^14 + 565868520 * q^15 + 268435456 * q^16 - 1355814414 * q^17 - 3166540416 * q^18 + 3783593180 * q^19 + 1482915840 * q^20 + 350112 * q^21 + 12273913344 * q^22 - 11608845528 * q^23 - 13111394304 * q^24 - 22325518025 * q^25 + 7652113664 * q^26 + 64956341880 * q^27 + 917504 * q^28 - 28959105930 * q^29 - 72431170560 * q^30 + 253685353952 * q^31 - 34359738368 * q^32 - 599503954896 * q^33 + 173544244992 * q^34 + 5068560 * q^35 + 405317173248 * q^36 + 817641294446 * q^37 - 484299927040 * q^38 - 373757926776 * q^39 - 189813227520 * q^40 - 682333284198 * q^41 - 44814336 * q^42 + 366945604292 * q^43 - 1571060908032 * q^44 + 2239090414470 * q^45 + 1485932227584 * q^46 + 695741581776 * q^47 + 1678258470912 * q^48 - 4747561506807 * q^49 + 2857666307200 * q^50 - 8476551716328 * q^51 - 979470548992 * q^52 + 12993372468702 * q^53 - 8314411760640 * q^54 - 8678999193480 * q^55 - 117440512 * q^56 + 23655024561360 * q^57 + 3706765559040 * q^58 + 9209035340340 * q^59 + 9271189831680 * q^60 - 42338641200298 * q^61 - 32471725305856 * q^62 + 1385361432 * q^63 + 4398046511104 * q^64 - 5410881310380 * q^65 + 76736506226688 * q^66 + 30029787950636 * q^67 - 22213663358976 * q^68 - 72578502241056 * q^69 - 648775680 * q^70 + 115328696975352 * q^71 - 51880598175744 * q^72 + 43787346432122 * q^73 - 104658085689088 * q^74 - 139579138692300 * q^75 + 61990390661120 * q^76 - 5369837088 * q^77 + 47841014627328 * q^78 + 79603813043120 * q^79 + 24296093122560 * q^80 + 51135221770281 * q^81 + 87338660377344 * q^82 - 3417068864868 * q^83 + 5736235008 * q^84 - 122714762611140 * q^85 - 46969037349376 * q^86 - 181052330274360 * q^87 + 201095796228096 * q^88 - 377306179184790 * q^89 - 286603573052160 * q^90 - 3347799728 * q^91 - 190199325130752 * q^92 + 1586040832907904 * q^93 - 89054922467328 * q^94 + 342453018721800 * q^95 - 214817084276736 * q^96 - 166982186657374 * q^97 + 607687872871296 * q^98 - 2372182779922956 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(2))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
2.16.a.a	$2$	$16$	2.a	1.a	$1$	$1$	$1$	$2.854$	\(\Q\)	None	✓	✓	✓	✓	2.16.a.a	$1$	$0$	\(-128\)	\(6252\)	\(90510\)	\(56\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}+6252q^{3}+2^{14}q^{4}+90510q^{5}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(2)) \simeq \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)