Space of modular forms of level 2, weight 24, and trivial character

• Label: 2.24.a
• Level: $2$
• Weight: $24$
• Character orbit: 2.a
• Rep. character: $\chi_{2}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(2))\).

	Total	New	Old
Modular forms	7	1	6
Cusp forms	5	1	4
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
\(+\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)

Trace form

q - 2048 * q^2 - 505908 * q^3 + 4194304 * q^4 - 90135570 * q^5 + 1036099584 * q^6 + 6872255096 * q^7 - 8589934592 * q^8 + 161799725637 * q^9 + 184597647360 * q^10 - 965328798588 * q^11 - 2121931948032 * q^12 + 542359999142 * q^13 - 14074378436608 * q^14 + 45600305947560 * q^15 + 17592186044416 * q^16 + 82083537265266 * q^17 - 331365838104576 * q^18 + 555748551616700 * q^19 - 378055981793280 * q^20 - 3476728831107168 * q^21 + 1976993379508224 * q^22 + 6508638190765032 * q^23 + 4345716629569536 * q^24 - 3796507975853225 * q^25 - 1110753278242816 * q^26 - 34227988283553480 * q^27 + 28824327038173184 * q^28 - 12202037915600490 * q^29 - 93389426580602880 * q^30 + 119978011042749152 * q^31 - 36028797018963968 * q^32 + 488367561836057904 * q^33 - 168107084319264768 * q^34 - 619434630263364720 * q^35 + 678637236438171648 * q^36 - 619510980267421234 * q^37 - 1138173033711001600 * q^38 - 274384262445930936 * q^39 + 774258650712637440 * q^40 - 1587735553771936038 * q^41 + 7120340646107480064 * q^42 + 8377717142038508132 * q^43 - 4048882441232842752 * q^44 - 14583910496134608090 * q^45 - 13329691014686785536 * q^46 + 13100457020745462096 * q^47 - 8900027657358409728 * q^48 + 19859142764417052873 * q^49 + 7775248334547404800 * q^50 - 41526718170796191528 * q^51 + 2274822713841287168 * q^52 + 41795979279875033022 * q^53 + 70098920004717527040 * q^54 + 87010461498144575160 * q^55 - 59032221774178680832 * q^56 - 281157638251301463600 * q^57 + 24989773651149803520 * q^58 - 74383865281405054380 * q^59 + 191261545637074698240 * q^60 - 271922036586947177098 * q^61 - 245714966615550263296 * q^62 + 1111928989040275096152 * q^63 + 73786976294838206464 * q^64 - 48885927667863680940 * q^65 - 1000176766640246587392 * q^66 + 1748137016509219336076 * q^67 + 344283308685854244864 * q^68 - 3292772129813555809056 * q^69 + 1268602122779370946560 * q^70 - 2717986658231940967368 * q^71 - 1389849060225375535104 * q^72 + 4312780994675837739962 * q^73 + 1268758487587678687232 * q^74 + 1920683757047953353300 * q^75 + 2330978373040131276800 * q^76 - 6633985755411940604448 * q^77 + 561938969489266556928 * q^78 + 3598562784411776110640 * q^79 - 1585681716659481477120 * q^80 + 2083872591752346472041 * q^81 + 3251682414124925005824 * q^82 - 225004177003815933828 * q^83 - 14582457643228119171072 * q^84 - 7398646419020992111620 * q^85 - 17157564706894864654336 * q^86 + 6173108597805612694920 * q^87 + 8292111239644861956096 * q^88 + 33892422870920675328810 * q^89 + 29867848696083677368320 * q^90 + 3727236267970165127632 * q^91 + 27299207198078536777728 * q^92 - 60697835610615137990016 * q^93 - 26829735978486706372608 * q^94 - 50092712476645676019000 * q^95 + 18227256642270023122944 * q^96 + 92121571514147280134306 * q^97 - 40671524381526124283904 * q^98 - 156189934761033233000556 * q^99

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(2))\) 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
2.24.a.a	$2$	$24$	2.a	1.a	$1$	$1$	$1$	$6.704$	\(\Q\)	None	✓	✓	✓	✓	2.24.a.a	$1$	$0$	\(-2048\)	\(-505908\)	\(-90135570\)	\(6872255096\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{11}q^{2}-505908q^{3}+2^{22}q^{4}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(2)) \simeq \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)