Space of modular forms of level 28, weight 7, and Character 28.b

• Label: 28.7.b
• Level: $28$
• Weight: $7$
• Character orbit: 28.b
• Rep. character: $\chi_{28}(13,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(28, [\chi])\).

	Total	New	Old
Modular forms	27	4	23
Cusp forms	21	4	17
Eisenstein series	6	0	6

Trace form

4 * q - 28 * q^7 - 156 * q^9 - 216 * q^11 + 768 * q^15 + 5376 * q^21 - 13752 * q^23 - 3548 * q^25 + 34920 * q^29 + 64512 * q^35 - 158936 * q^37 - 60672 * q^39 + 215080 * q^43 + 320068 * q^49 - 665088 * q^51 - 158040 * q^53 + 689664 * q^57 + 791364 * q^63 - 1631232 * q^65 - 511000 * q^67 + 1648584 * q^71 + 1582056 * q^77 - 2827768 * q^79 - 652860 * q^81 + 1878528 * q^85 + 1752576 * q^91 - 3838464 * q^93 - 1094400 * q^95 + 3169512 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(28, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.7.b.a	$28$	$7$	28.b	7.b	$2$	$4$	$4$	$6.442$	4.0.903168.1	None		✓	✓	✓	28.7.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-28\)	$2^{7}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-7-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

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