Space of modular forms of level 10, weight 3, and Character 10.c

• Label: 10.3.c
• Level: $10$
• Weight: $3$
• Character orbit: 10.c
• Rep. character: $\chi_{10}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(10, [\chi])\).

	Total	New	Old
Modular forms	10	2	8
Cusp forms	2	2	0
Eisenstein series	8	0	8

Trace form

2 * q - 2 * q^2 - 4 * q^3 + 8 * q^6 + 4 * q^7 + 4 * q^8 - 10 * q^10 - 16 * q^11 - 8 * q^12 + 6 * q^13 + 20 * q^15 - 8 * q^16 + 14 * q^17 + 2 * q^18 + 20 * q^20 - 16 * q^21 + 16 * q^22 - 4 * q^23 - 50 * q^25 - 12 * q^26 - 40 * q^27 - 8 * q^28 + 104 * q^31 + 8 * q^32 + 32 * q^33 + 20 * q^35 - 4 * q^36 - 6 * q^37 - 40 * q^38 - 20 * q^40 - 16 * q^41 + 16 * q^42 - 84 * q^43 + 10 * q^45 + 8 * q^46 - 36 * q^47 + 16 * q^48 + 50 * q^50 - 56 * q^51 + 12 * q^52 + 106 * q^53 + 16 * q^56 + 80 * q^57 + 80 * q^58 - 40 * q^60 - 96 * q^61 - 104 * q^62 - 4 * q^63 - 30 * q^65 - 64 * q^66 + 124 * q^67 - 28 * q^68 - 40 * q^70 - 56 * q^71 + 4 * q^72 - 94 * q^73 + 100 * q^75 + 80 * q^76 - 32 * q^77 + 24 * q^78 + 142 * q^81 + 16 * q^82 + 36 * q^83 + 70 * q^85 + 168 * q^86 - 160 * q^87 - 32 * q^88 - 10 * q^90 + 24 * q^91 - 8 * q^92 - 208 * q^93 - 200 * q^95 - 32 * q^96 - 126 * q^97 - 82 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(10, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.3.c.a	$10$	$3$	10.c	5.c	$4$	$2$	$1$	$0.272$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	10.3.c.a	$2$	$0$	\(-2\)	\(-4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}+(2 i-2)q^{3}+2 i q^{4}+\cdots\)