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

• Label: 28.5.c
• Level: $28$
• Weight: $5$
• Character orbit: 28.c
• Rep. character: $\chi_{28}(15,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
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	18	12	6
Cusp forms	14	12	2
Eisenstein series	4	0	4

Trace form

12 * q + 3 * q^2 - 31 * q^4 + 24 * q^5 + 30 * q^6 + 171 * q^8 - 436 * q^9 + 52 * q^10 + 390 * q^12 + 120 * q^13 + 147 * q^14 - 911 * q^16 - 648 * q^17 + 631 * q^18 + 912 * q^20 - 628 * q^22 - 1174 * q^24 + 2340 * q^25 - 2280 * q^26 + 245 * q^28 + 24 * q^29 + 800 * q^30 + 1443 * q^32 - 1120 * q^33 + 1634 * q^34 + 421 * q^36 - 424 * q^37 + 2970 * q^38 - 4936 * q^40 + 7320 * q^41 - 2450 * q^42 - 2244 * q^44 + 888 * q^45 - 7512 * q^46 + 3550 * q^48 - 4116 * q^49 - 5451 * q^50 - 3484 * q^52 - 7080 * q^53 + 11620 * q^54 + 3087 * q^56 - 9152 * q^57 + 4666 * q^58 + 15856 * q^60 + 9752 * q^61 - 5964 * q^62 + 6329 * q^64 - 11280 * q^65 + 30264 * q^66 - 7314 * q^68 - 10464 * q^69 - 7644 * q^70 - 10553 * q^72 + 13752 * q^73 - 2838 * q^74 + 11202 * q^76 + 4704 * q^77 - 34600 * q^78 - 49272 * q^80 + 3340 * q^81 - 11950 * q^82 + 11662 * q^84 + 23152 * q^85 + 30612 * q^86 + 20740 * q^88 - 12552 * q^89 - 40508 * q^90 + 47880 * q^92 + 13632 * q^93 + 71340 * q^94 - 11110 * q^96 + 19704 * q^97 - 1029 * q^98

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.c.a	$28$	$5$	28.c	4.b	$2$	$12$	$12$	$2.894$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	28.5.c.a	$2$	$0$	\(3\)	\(0\)	\(24\)	\(0\)	$2^{20}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-3+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)

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

\( S_{5}^{\mathrm{old}}(28, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)