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

• Label: 28.5.h
• Level: $28$
• Weight: $5$
• Character orbit: 28.h
• Rep. character: $\chi_{28}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• 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.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
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	38	6	32
Cusp forms	26	6	20
Eisenstein series	12	0	12

Trace form

6 * q + 9 * q^3 - 27 * q^5 + 66 * q^7 + 90 * q^9 + 135 * q^11 - 486 * q^15 - 1107 * q^17 - 747 * q^19 + 2169 * q^21 + 243 * q^23 + 1878 * q^25 - 540 * q^29 - 5355 * q^31 - 1863 * q^33 + 6021 * q^35 + 2355 * q^37 + 6588 * q^39 - 948 * q^43 - 14418 * q^45 - 9747 * q^47 + 8430 * q^49 - 891 * q^51 + 6291 * q^53 - 6894 * q^57 - 2943 * q^59 + 4041 * q^61 + 15138 * q^63 + 7668 * q^65 + 1659 * q^67 + 2268 * q^71 - 8703 * q^73 - 3438 * q^75 - 10665 * q^77 - 7773 * q^79 - 7479 * q^81 - 702 * q^85 + 40014 * q^87 + 14985 * q^89 - 20952 * q^91 + 1449 * q^93 - 20655 * q^95 + 8100 * 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.h.a	$28$	$5$	28.h	7.d	$6$	$6$	$3$	$2.894$	6.0.11337408.1	None		✓	✓	✓	28.5.h.a	$2$	$0$	\(0\)	\(9\)	\(-27\)	\(66\)	$2^{2}\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\beta _{1}+\beta _{3})q^{3}+(-3-3\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

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

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