Space of modular forms of level 28, weight 12, and Character 28.e

• Label: 28.12.e
• Level: $28$
• Weight: $12$
• Character orbit: 28.e
• Rep. character: $\chi_{28}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	28.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(28, [\chi])\).

	Total	New	Old
Modular forms	94	14	80
Cusp forms	82	14	68
Eisenstein series	12	0	12

Trace form

\( 14 q + 243 q^{3} + 3719 q^{5} - 83356 q^{7} - 294938 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(28, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.12.e.a	$28$	$12$	28.e	7.c	$3$	$14$	$7$	$21.514$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(243\)	\(3719\)	\(-83356\)	$2^{42}\cdot 3^{5}\cdot 7^{11}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(35\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(531-531\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)