Space of modular forms of level 21, weight 4, and Character 21.e

• Label: 21.4.e
• Level: $21$
• Weight: $4$
• Character orbit: 21.e
• Rep. character: $\chi_{21}(4,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $10$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(10\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(21, [\chi])\).

	Total	New	Old
Modular forms	20	8	12
Cusp forms	12	8	4
Eisenstein series	8	0	8

Trace form

8 * q + 2 * q^2 + 6 * q^3 - 26 * q^4 - 8 * q^5 - 24 * q^6 - 20 * q^7 + 120 * q^8 - 36 * q^9 + 46 * q^10 - 20 * q^11 + 72 * q^12 - 4 * q^13 - 242 * q^14 - 84 * q^15 - 170 * q^16 - 132 * q^17 + 18 * q^18 + 218 * q^19 + 872 * q^20 + 108 * q^21 + 76 * q^22 - 132 * q^23 + 54 * q^24 - 14 * q^25 - 466 * q^26 - 108 * q^27 - 166 * q^28 - 488 * q^29 - 192 * q^30 + 348 * q^31 - 728 * q^32 + 150 * q^33 - 552 * q^34 + 140 * q^35 + 468 * q^36 + 54 * q^37 + 350 * q^38 + 378 * q^39 + 42 * q^40 + 1208 * q^41 - 156 * q^42 + 772 * q^43 + 920 * q^44 - 72 * q^45 + 804 * q^46 + 240 * q^47 - 1872 * q^48 - 940 * q^49 - 2060 * q^50 - 108 * q^51 - 260 * q^52 - 756 * q^53 + 108 * q^54 - 1972 * q^55 + 1152 * q^56 + 1116 * q^57 + 358 * q^58 - 1128 * q^59 + 1326 * q^60 + 188 * q^61 + 3636 * q^62 - 126 * q^63 + 68 * q^64 + 280 * q^65 - 156 * q^66 + 998 * q^67 - 2028 * q^68 - 1800 * q^69 + 3566 * q^70 - 48 * q^71 - 540 * q^72 - 1350 * q^73 - 1950 * q^74 + 738 * q^75 - 4712 * q^76 + 548 * q^77 - 492 * q^78 - 1328 * q^79 - 388 * q^80 - 324 * q^81 + 956 * q^82 + 1992 * q^83 + 1536 * q^84 + 3096 * q^85 + 3286 * q^86 + 1050 * q^87 + 1206 * q^88 - 2672 * q^89 - 828 * q^90 - 206 * q^91 - 1512 * q^92 + 474 * q^93 + 3204 * q^94 + 688 * q^95 + 1914 * q^96 + 1044 * q^97 - 5884 * q^98 + 360 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(21, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.4.e.a	$21$	$4$	21.e	7.c	$3$	$2$	$1$	$1.239$	\(\Q(\sqrt{-3}) \)	None		✓			21.4.e.a	$2$	$0$	\(3\)	\(-3\)	\(3\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{2}-3\zeta_{6}q^{3}-\zeta_{6}q^{4}+(3+\cdots)q^{5}+\cdots\)
21.4.e.b	$21$	$4$	21.e	7.c	$3$	$6$	$3$	$1.239$	6.0.9924270768.1	None		✓	✓		21.4.e.b	$2$	$0$	\(-1\)	\(9\)	\(-11\)	\(-13\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(3-3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(21, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)