Space of modular forms of level 1, weight 24, and trivial character

• Label: 1.24.a
• Level: $1$
• Weight: $24$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	3	3	0
Cusp forms	2	2	0
Eisenstein series	1	1	0

Trace form

2 * q + 1080 * q^2 + 339480 * q^3 + 25326656 * q^4 + 73069020 * q^5 - 1809673056 * q^6 - 1359184400 * q^7 + 49459023360 * q^8 - 34999394166 * q^9 - 585013636080 * q^10 + 856801968264 * q^11 + 2146514952960 * q^12 + 4376109322060 * q^13 - 41666034529728 * q^14 + 42377338985040 * q^15 + 15956586401792 * q^16 + 254028147597540 * q^17 - 695480683916520 * q^18 + 4260600979960 * q^19 + 250868387468160 * q^20 + 1734031637722944 * q^21 + 2068343882177760 * q^22 - 8144713079008560 * q^23 - 1286622315141120 * q^24 - 11780274628800850 * q^25 + 55025854658735184 * q^26 - 5424634982716560 * q^27 - 61418438819709440 * q^28 + 20818433601623340 * q^29 - 155926924188644160 * q^30 + 137714017177000384 * q^31 + 353265663781601280 * q^32 + 68361366766001760 * q^33 - 839483655961325328 * q^34 + 565961271250425120 * q^35 - 1173916300077574848 * q^36 - 897721264408967780 * q^37 + 5699708971590961440 * q^38 - 1785011473665029232 * q^39 - 1226668524414336000 * q^40 - 2294435477168314956 * q^41 - 4657011326437397760 * q^42 - 1750760768619855800 * q^43 + 12584088840033038592 * q^44 + 8897092690294206540 * q^45 - 8813206018050221376 * q^46 + 15759744217656780960 * q^47 - 33749519399576616960 * q^48 - 13461981704376200814 * q^49 - 51990825483785316600 * q^50 + 89998362845078292144 * q^51 + 112291883783912022400 * q^52 - 140287253401646796420 * q^53 + 104731223417039799360 * q^54 + 7153550955060182640 * q^55 - 232456712054288117760 * q^56 - 272752401448627175520 * q^57 + 293749486923568689360 * q^58 + 280872989971340771880 * q^59 + 343522601114937592320 * q^60 - 180452892516502223636 * q^61 - 540743475843874103040 * q^62 + 690775113933935014320 * q^63 - 893690254469352914944 * q^64 - 632168834809440380760 * q^65 - 544338140913651883392 * q^66 + 1754233163431557625240 * q^67 + 2162050190142944330880 * q^68 - 1170560672172404223552 * q^69 - 765428657799921252480 * q^70 + 3055033510194143328624 * q^71 - 4152294352103038548480 * q^72 - 8063408253877606149260 * q^73 + 6715344283148807757072 * q^74 + 190631089350520885800 * q^75 + 6207154294513080590080 * q^76 - 2165184764357449665600 * q^77 + 3614293948840808587200 * q^78 + 6244916814559639980640 * q^79 - 10840537585501794017280 * q^80 - 2793528580929833975598 * q^81 - 24457792891615712450640 * q^82 + 6875994082418498976120 * q^83 + 15917751907190402476032 * q^84 + 23969743087870314902520 * q^85 - 10916288812918999243296 * q^86 - 10026640653837674384880 * q^87 + 28988514668199273707520 * q^88 + 6395093086173070004820 * q^89 - 8986073954327865866160 * q^90 - 54890178162704560146016 * q^91 - 107907439017191756981760 * q^92 + 52900811441357852079360 * q^93 + 159400518006534931827072 * q^94 - 85533361066700858502000 * q^95 + 105592121669584394256384 * q^96 - 31147288846254030500540 * q^97 + 48364767616374671003640 * q^98 - 41158245132312135981912 * q^99

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.24.a.a	$1$	$24$	1.a	1.a	$1$	$2$	$2$	$3.352$	\(\Q(\sqrt{144169}) \)	None	✓	✓	✓	✓	1.24.a.a	$1$	$0$	\(1080\)	\(339480\)	\(73069020\)	\(-1359184400\)	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+(540-\beta )q^{2}+(169740+48\beta )q^{3}+\cdots\)