Space of modular forms of level 72, weight 21, and Character 72.b

• Label: 72.21.b
• Level: $72$
• Weight: $21$
• Character orbit: 72.b
• Rep. character: $\chi_{72}(19,\cdot)$
• Character field: $\Q$
• Dimension: $99$
• Newform subspaces: $4$
• Sturm bound: $252$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(252\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(72, [\chi])\).

	Total	New	Old
Modular forms	244	101	143
Cusp forms	236	99	137
Eisenstein series	8	2	6

Trace form

99 * q + 628 * q^2 - 267504 * q^4 + 609676444 * q^8 - 10300080972 * q^10 - 14520628702 * q^11 + 347346537852 * q^14 + 3184617175248 * q^16 + 990389375402 * q^17 + 1375336086078 * q^19 - 16712772648648 * q^20 + 35786555301372 * q^22 - 1826238951618285 * q^25 + 169480344502272 * q^26 + 483694274694696 * q^28 + 3003613602435448 * q^32 + 1181918888641440 * q^34 + 3234393426905664 * q^35 - 21464478253103428 * q^38 - 59241470432225400 * q^40 - 2320164587283094 * q^41 - 34061137878160098 * q^43 - 38995922279897272 * q^44 - 59994246611399592 * q^46 - 1035109767928302525 * q^49 + 134551905327436156 * q^50 - 194020495051695936 * q^52 - 97204960107400152 * q^56 - 1140184757694411708 * q^58 + 1954151757601224098 * q^59 - 1607493854454198444 * q^62 - 1755455458389329808 * q^64 + 1574962450473910464 * q^65 + 1773610782729036030 * q^67 - 7860075384249332344 * q^68 + 9306089451940535112 * q^70 + 4497851542813262598 * q^73 + 30820581065840354328 * q^74 + 20783302310026584648 * q^76 + 56304248333026034208 * q^80 - 37586343012509615880 * q^82 + 10452525070055080322 * q^83 - 18356698016612978740 * q^86 + 17872718167235001168 * q^88 + 43617150548200737482 * q^89 - 15970522797644366976 * q^91 + 64406406827025718944 * q^92 + 7351803603366172248 * q^94 - 12927415363175728026 * q^97 - 64399653240512616308 * q^98

Decomposition of \(S_{21}^{\mathrm{new}}(72, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.21.b.a	$72$	$21$	72.b	8.d	$2$	$1$	$1$	$182.530$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓				8.21.d.a	$2$	$0$	\(-1024\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{10}q^{2}+2^{20}q^{4}-2^{30}q^{8}+42383023726q^{11}+\cdots\)
72.21.b.b	$72$	$21$	72.b	8.d	$2$	$18$	$18$	$182.530$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None					8.21.d.b	$2$	$0$	\(398\)	\(0\)	\(0\)	\(0\)	$2^{153}\cdot 3^{19}\cdot 5^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(22+\beta _{1})q^{2}+(40275+21\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
72.21.b.c	$72$	$21$	72.b	8.d	$2$	$40$	$40$	$182.530$		None		✓			72.21.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
72.21.b.d	$72$	$21$	72.b	8.d	$2$	$40$	$40$	$182.530$		None					24.21.b.a	$2$	$0$	\(1254\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{21}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{21}^{\mathrm{old}}(72, [\chi]) \simeq \) \(S_{21}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)