Space of modular forms of level 6, weight 21, and Character 6.b

• Label: 6.21.b
• Level: $6$
• Weight: $21$
• Character orbit: 6.b
• Rep. character: $\chi_{6}(5,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $21$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(21\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(6, [\chi])\).

	Total	New	Old
Modular forms	22	6	16
Cusp forms	18	6	12
Eisenstein series	4	0	4

Trace form

6 * q + 18846 * q^3 - 3145728 * q^4 + 35057664 * q^6 - 566671812 * q^7 + 1944941382 * q^9 + 5360984064 * q^10 - 9880731648 * q^12 - 49898545620 * q^13 + 487708151328 * q^15 + 1649267441664 * q^16 - 3239129751552 * q^18 + 15927597287292 * q^19 - 20677554127188 * q^21 + 21184189636608 * q^22 - 18380312543232 * q^24 + 337510512308454 * q^25 - 1019514529044162 * q^27 + 297099230969856 * q^28 - 920809286295552 * q^30 + 1832545426397628 * q^31 - 3503562514347744 * q^33 + 2508713101983744 * q^34 - 1019709427286016 * q^36 + 424332326872812 * q^37 + 13854943345637340 * q^39 - 2810699612946432 * q^40 + 30169507188989952 * q^42 - 49488752333951556 * q^43 + 64297936569436992 * q^45 - 51218624034717696 * q^46 + 5180349034266624 * q^48 - 185965132589503470 * q^49 + 114461935953291648 * q^51 + 26161208686018560 * q^52 - 103567464750919680 * q^54 + 468503586680075712 * q^55 - 1250127589109383188 * q^57 + 330130684975472640 * q^58 - 255699531243454464 * q^60 + 3301830012872093484 * q^61 - 724019288731292484 * q^63 - 864691128455135232 * q^64 + 1110947414199017472 * q^66 - 2779226272508556228 * q^67 + 667934407322175168 * q^69 - 1866219302039371776 * q^70 + 1698236859181694976 * q^72 - 9149401536792501300 * q^73 + 9127347583517050878 * q^75 - 8350648126559748096 * q^76 + 19815256334884331520 * q^78 + 90056048403257148 * q^79 - 13310358127786728378 * q^81 - 19709381871486517248 * q^82 + 10840993498235142144 * q^84 + 78223886062534003968 * q^85 - 87334395308747540640 * q^87 - 11106616416197935104 * q^88 + 60406983770669457408 * q^90 + 132462766690215009720 * q^91 - 157075923546140581332 * q^93 - 106728395801434030080 * q^94 + 9636577302666018816 * q^96 + 92028905119987573836 * q^97 - 224342570810992842432 * q^99

Decomposition of \(S_{21}^{\mathrm{new}}(6, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6.21.b.a	$6$	$21$	6.b	3.b	$2$	$6$	$6$	$15.211$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		✓	✓	✓	6.21.b.a	$2$	$0$	\(0\)	\(18846\)	\(0\)	\(-566671812\)	$2^{31}\cdot 3^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(3141-11\beta _{1}-\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{21}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

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