Space of modular forms of level 24, weight 28, and Character 24.f

• Label: 24.28.f
• Level: $24$
• Weight: $28$
• Character orbit: 24.f
• Rep. character: $\chi_{24}(11,\cdot)$
• Character field: $\Q$
• Dimension: $106$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$24 = 2^{3} \cdot 3$
Weight:	$k$	$=$	$28$
Character orbit:	$[\chi]$	$=$	24.f (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$24$
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$112$
Trace bound:			$1$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{28}(24, [\chi])$.

	Total	New	Old
Modular forms	110	110	0
Cusp forms	106	106	0
Eisenstein series	4	4	0

Trace form

106 * q - 2 * q^3 + 118953412 * q^4 - 29615742008 * q^6 - 2 * q^9 - 11696046941304 * q^10 + 833046350880916 * q^12 + 90275072969320 * q^16 - 234338308101394376 * q^18 - 361273435637780380 * q^19 - 2716164181482802816 * q^22 - 3320436517261267640 * q^24 + 146031379699707031246 * q^25 + 16968274332320900026 * q^27 - 64802173230062700912 * q^28 + 121976691666319684176 * q^30 - 2632575711256057504 * q^33 + 109067432386588281968 * q^34 + 530142361225984950604 * q^36 - 7893933656518536719328 * q^40 + 11744252006007279620040 * q^42 - 14200115812612743847252 * q^43 - 36010569275877185639136 * q^46 - 178122222708366231496520 * q^48 - 825819634460874635230250 * q^49 + 62120836396250542956272 * q^51 - 442783254290529153653568 * q^52 + 411495469774191220854808 * q^54 - 275113126452436693837804 * q^57 + 430639113796083234682344 * q^58 + 2126303856333605132718000 * q^60 + 11162554382786085248008624 * q^64 - 18537552773258476852539160 * q^66 - 16791855426275982771219556 * q^67 - 29404244700669557820006864 * q^70 - 32677907530310337652297520 * q^72 + 6425348165429409878800532 * q^73 - 68365725821360739276484838 * q^75 + 6561606820671805224035480 * q^76 - 53289960447911890953260976 * q^78 - 31880826074766791642298758 * q^81 - 121391761928980436494476736 * q^82 - 154782558650154535863594240 * q^84 - 220967974220292151399000912 * q^88 + 853672785457912285624427304 * q^90 + 602709767970401640299590368 * q^91 + 2279573344482043094174236608 * q^94 + 2821951986727434061814868880 * q^96 - 1110522253821305274003465652 * q^97 + 2074549009847927035532477840 * q^99

Decomposition of $S_{28}^{\mathrm{new}}(24, [\chi])$ 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
24.28.f.a	$24$	$28$	24.f	24.f	$2$	$2$	$2$	$110.845$	$\Q(\sqrt{-2})$	$\Q(\sqrt{-2})$		✓			24.28.f.a	$4$	$0$	$0$	$-4360310$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{13}\beta q^{2}+(-2180155+1198441\beta )q^{3}+\cdots$
24.28.f.b	$24$	$28$	24.f	24.f	$2$	$104$	$104$	$110.845$		None		✓	✓		24.28.f.b	$4$	$0$	$0$	$4360308$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$