Space of modular forms of level 1, weight 12, and trivial character

• Label: 1.12.a
• Level: $1$
• Weight: $12$
• 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:	\( k \)	\(=\)	\( 12 \)
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 \(M_{12}(\Gamma_0(1))\).

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

Trace form

q - 24 * q^2 + 252 * q^3 - 1472 * q^4 + 4830 * q^5 - 6048 * q^6 - 16744 * q^7 + 84480 * q^8 - 113643 * q^9 - 115920 * q^10 + 534612 * q^11 - 370944 * q^12 - 577738 * q^13 + 401856 * q^14 + 1217160 * q^15 + 987136 * q^16 - 6905934 * q^17 + 2727432 * q^18 + 10661420 * q^19 - 7109760 * q^20 - 4219488 * q^21 - 12830688 * q^22 + 18643272 * q^23 + 21288960 * q^24 - 25499225 * q^25 + 13865712 * q^26 - 73279080 * q^27 + 24647168 * q^28 + 128406630 * q^29 - 29211840 * q^30 - 52843168 * q^31 - 196706304 * q^32 + 134722224 * q^33 + 165742416 * q^34 - 80873520 * q^35 + 167282496 * q^36 - 182213314 * q^37 - 255874080 * q^38 - 145589976 * q^39 + 408038400 * q^40 + 308120442 * q^41 + 101267712 * q^42 - 17125708 * q^43 - 786948864 * q^44 - 548895690 * q^45 - 447438528 * q^46 + 2687348496 * q^47 + 248758272 * q^48 - 1696965207 * q^49 + 611981400 * q^50 - 1740295368 * q^51 + 850430336 * q^52 - 1596055698 * q^53 + 1758697920 * q^54 + 2582175960 * q^55 - 1414533120 * q^56 + 2686677840 * q^57 - 3081759120 * q^58 - 5189203740 * q^59 - 1791659520 * q^60 + 6956478662 * q^61 + 1268236032 * q^62 + 1902838392 * q^63 + 2699296768 * q^64 - 2790474540 * q^65 - 3233333376 * q^66 - 15481826884 * q^67 + 10165534848 * q^68 + 4698104544 * q^69 + 1940964480 * q^70 + 9791485272 * q^71 - 9600560640 * q^72 + 1463791322 * q^73 + 4373119536 * q^74 - 6425804700 * q^75 - 15693610240 * q^76 - 8951543328 * q^77 + 3494159424 * q^78 + 38116845680 * q^79 + 4767866880 * q^80 + 1665188361 * q^81 - 7394890608 * q^82 - 29335099668 * q^83 + 6211086336 * q^84 - 33355661220 * q^85 + 411016992 * q^86 + 32358470760 * q^87 + 45164021760 * q^88 - 24992917110 * q^89 + 13173496560 * q^90 + 9673645072 * q^91 - 27442896384 * q^92 - 13316478336 * q^93 - 64496363904 * q^94 + 51494658600 * q^95 - 49569988608 * q^96 + 75013568546 * q^97 + 40727164968 * q^98 - 60754911516 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.12.a.a	$1$	$12$	1.a	1.a	$1$	$1$	$1$	$0.768$	\(\Q\)	None	✓	✓	✓	✓	1.12.a.a	$1$	$0$	\(-24\)	\(252\)	\(4830\)	\(-16744\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-24q^{2}+252q^{3}-1472q^{4}+4830q^{5}+\cdots\)