Space of modular forms of level 28, weight 6, and Character 28.e

• Label: 28.6.e
• Level: $28$
• Weight: $6$
• Character orbit: 28.e
• Rep. character: $\chi_{28}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	28.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(28, [\chi])\).

	Total	New	Old
Modular forms	46	6	40
Cusp forms	34	6	28
Eisenstein series	12	0	12

Trace form

6 * q - 9 * q^3 - 61 * q^5 - 28 * q^7 - 242 * q^9 - 101 * q^11 - 724 * q^13 + 3070 * q^15 - 1049 * q^17 - 1767 * q^19 - 1127 * q^21 + 2953 * q^23 + 284 * q^25 + 6822 * q^27 + 10940 * q^29 - 4837 * q^31 - 24439 * q^33 - 30905 * q^35 + 7215 * q^37 + 24838 * q^39 + 3876 * q^41 + 73224 * q^43 - 41470 * q^45 - 34299 * q^47 - 74970 * q^49 + 21629 * q^51 + 23691 * q^53 + 61414 * q^55 + 174714 * q^57 - 81001 * q^59 - 111625 * q^61 - 145698 * q^63 + 70950 * q^65 + 61327 * q^67 + 49706 * q^69 + 124096 * q^71 - 24533 * q^73 - 142172 * q^75 - 67123 * q^77 - 34207 * q^79 + 43429 * q^81 - 106712 * q^83 + 101806 * q^85 - 5378 * q^87 - 114405 * q^89 - 75544 * q^91 + 95641 * q^93 - 29249 * q^95 + 284740 * q^97 + 206284 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(28, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.6.e.a	$28$	$6$	28.e	7.c	$3$	$2$	$1$	$4.491$	\(\Q(\sqrt{-3}) \)	None		✓			28.6.e.a	$2$	$0$	\(0\)	\(19\)	\(-19\)	\(-140\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+19\zeta_{6}q^{3}+(-19+19\zeta_{6})q^{5}+(-133+\cdots)q^{7}+\cdots\)
28.6.e.b	$28$	$6$	28.e	7.c	$3$	$4$	$2$	$4.491$	\(\Q(\sqrt{-3}, \sqrt{109})\)	None		✓	✓		28.6.e.b	$2$	$0$	\(0\)	\(-28\)	\(-42\)	\(112\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-14+14\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-21\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(28, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)