Space of modular forms of level 18, weight 21, and Character 18.b

• Label: 18.21.b
• Level: $18$
• Weight: $21$
• Character orbit: 18.b
• Rep. character: $\chi_{18}(17,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $63$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	18.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(63\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(18, [\chi])\).

	Total	New	Old
Modular forms	64	8	56
Cusp forms	56	8	48
Eisenstein series	8	0	8

Trace form

8 * q - 4194304 * q^4 + 599424160 * q^7 - 13746831360 * q^10 - 258508597760 * q^13 + 2199023255552 * q^16 - 18413226146432 * q^19 + 947650560000 * q^22 - 581762885173000 * q^25 - 314270893998080 * q^28 - 3001252967864288 * q^31 - 4202434243067904 * q^34 + 1310832890517040 * q^37 + 7207298720071680 * q^40 + 99703523115330880 * q^43 + 74972972105859072 * q^46 - 21819252030947976 * q^49 + 135532955702394880 * q^52 - 623813442151590720 * q^55 - 983646357348679680 * q^58 - 626564790143754800 * q^61 - 1152921504606846976 * q^64 - 3216237405168944960 * q^67 + 10956067854782300160 * q^70 + 6357264084843717760 * q^73 + 9653833509860540416 * q^76 + 18138137944168385248 * q^79 + 15241577659713454080 * q^82 - 118681935262238522160 * q^85 - 496841816801280000 * q^88 - 55926193727090753536 * q^91 + 177354186184835727360 * q^94 - 486767814027851851520 * q^97

Decomposition of \(S_{21}^{\mathrm{new}}(18, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.21.b.a	$18$	$21$	18.b	3.b	$2$	$4$	$4$	$45.632$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		✓			18.21.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(196612688\)	$2^{9}\cdot 3^{10}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{9}\beta _{1}q^{2}-2^{19}q^{4}+(-793635\beta _{1}+\cdots)q^{5}+\cdots\)
18.21.b.b	$18$	$21$	18.b	3.b	$2$	$4$	$4$	$45.632$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		✓			18.21.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(402811472\)	$2^{9}\cdot 3^{8}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{9}\beta _{1}q^{2}-2^{19}q^{4}+(-4149795\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{21}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

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