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

• Label: 5.5.c
• Level: $5$
• Weight: $5$
• Character orbit: 5.c
• Rep. character: $\chi_{5}(2,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

Trace form

2 * q - 2 * q^2 - 12 * q^3 + 40 * q^5 + 24 * q^6 - 52 * q^7 - 60 * q^8 - 10 * q^10 - 16 * q^11 + 168 * q^12 + 278 * q^13 - 420 * q^15 - 328 * q^16 - 2 * q^17 + 18 * q^18 + 420 * q^20 + 624 * q^21 + 16 * q^22 - 332 * q^23 + 350 * q^25 - 556 * q^26 - 1080 * q^27 - 728 * q^28 + 480 * q^30 + 1144 * q^31 + 1288 * q^32 + 96 * q^33 - 260 * q^35 + 252 * q^36 - 502 * q^37 + 360 * q^38 - 2100 * q^40 - 3376 * q^41 - 624 * q^42 + 2948 * q^43 - 270 * q^45 + 664 * q^46 + 4948 * q^47 + 1968 * q^48 + 850 * q^50 + 24 * q^51 - 3892 * q^52 - 6662 * q^53 - 320 * q^55 + 3120 * q^56 - 2160 * q^57 - 960 * q^58 + 840 * q^60 + 3184 * q^61 - 1144 * q^62 + 468 * q^63 + 9730 * q^65 - 192 * q^66 + 1748 * q^67 - 28 * q^68 - 1560 * q^70 - 12136 * q^71 - 540 * q^72 - 1582 * q^73 - 9300 * q^75 + 5040 * q^76 + 416 * q^77 + 3336 * q^78 - 6560 * q^80 + 11502 * q^81 + 3376 * q^82 + 11308 * q^83 - 10 * q^85 - 5896 * q^86 + 5760 * q^87 + 480 * q^88 + 630 * q^90 - 14456 * q^91 + 4648 * q^92 - 6864 * q^93 - 5400 * q^95 - 15456 * q^96 - 13102 * q^97 - 2098 * q^98

Decomposition of \(S_{5}^{\mathrm{new}}(5, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5.5.c.a	$5$	$5$	5.c	5.c	$4$	$2$	$1$	$0.517$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	5.5.c.a	$2$	$0$	\(-2\)	\(-12\)	\(40\)	\(-52\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}+(6 i-6)q^{3}-14 i q^{4}+\cdots\)