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

• Label: 72.21.e
• Level: $72$
• Weight: $21$
• Character orbit: 72.e
• Rep. character: $\chi_{72}(17,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $252$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	72.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(252\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	248	20	228
Cusp forms	232	20	212
Eisenstein series	16	0	16

Trace form

20 * q + 187327248 * q^7 - 164244011776 * q^13 - 13445754640448 * q^19 - 388496127759764 * q^25 - 423277661451824 * q^31 - 8666443278779016 * q^37 + 6638936174186528 * q^43 + 323507482795406764 * q^49 + 1036940790126597344 * q^55 - 1558532070186926968 * q^61 - 9196308102489129248 * q^67 - 5272181656521318592 * q^73 + 29568317256866220464 * q^79 + 30723131637520765960 * q^85 - 9714721370964547584 * q^91 + 23825970708940358272 * q^97

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.e.a	$72$	$21$	72.e	3.b	$2$	$10$	$10$	$182.530$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			72.21.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-489367704\)	$2^{76}\cdot 3^{28}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(732773\beta _{5}+\beta _{6})q^{5}+(-48936770+\cdots)q^{7}+\cdots\)
72.21.e.b	$72$	$21$	72.e	3.b	$2$	$10$	$10$	$182.530$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			72.21.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(676694952\)	$2^{77}\cdot 3^{28}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-806622\beta _{5}+\beta _{6})q^{5}+(67669493+\cdots)q^{7}+\cdots\)

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

\( S_{21}^{\mathrm{old}}(72, [\chi]) \simeq \) \(S_{21}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)