Space of modular forms of level 28, weight 5, and Character 28.b

• Label: 28.5.b
• Level: $28$
• Weight: $5$
• Character orbit: 28.b
• Rep. character: $\chi_{28}(13,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	28.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(28, [\chi])\).

	Total	New	Old
Modular forms	19	2	17
Cusp forms	13	2	11
Eisenstein series	6	0	6

Trace form

2 * q - 14 * q^7 + 66 * q^9 + 36 * q^11 - 288 * q^15 - 672 * q^21 + 1476 * q^23 + 386 * q^25 - 1692 * q^29 - 2016 * q^35 + 4772 * q^37 + 1824 * q^39 - 5020 * q^43 - 4606 * q^49 + 5760 * q^51 - 540 * q^53 - 1248 * q^57 - 462 * q^63 + 5472 * q^65 + 4900 * q^67 - 6300 * q^71 - 252 * q^77 - 7964 * q^79 - 5598 * q^81 + 17280 * q^85 + 12768 * q^91 - 16128 * q^93 - 3744 * q^95 + 1188 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(28, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.5.b.a	$28$	$5$	28.b	7.b	$2$	$2$	$2$	$2.894$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	28.5.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-14\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-3\beta q^{5}+(-7\beta-7)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(28, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)