Space of modular forms of level 15, weight 3, and Character 15.c

• Label: 15.3.c
• Level: $15$
• Weight: $3$
• Character orbit: 15.c
• Rep. character: $\chi_{15}(11,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	15.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(15, [\chi])\).

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

Trace form

2 * q - 4 * q^3 - 2 * q^4 + 10 * q^6 - 12 * q^7 - 2 * q^9 + 10 * q^10 + 4 * q^12 + 32 * q^13 - 10 * q^15 - 38 * q^16 - 40 * q^18 - 4 * q^19 + 24 * q^21 + 20 * q^22 + 30 * q^24 - 10 * q^25 + 44 * q^27 + 12 * q^28 - 20 * q^30 - 36 * q^31 - 20 * q^33 + 20 * q^34 + 2 * q^36 - 32 * q^37 - 64 * q^39 + 30 * q^40 - 60 * q^42 + 32 * q^43 + 40 * q^45 + 60 * q^46 + 76 * q^48 - 26 * q^49 - 20 * q^51 - 32 * q^52 + 70 * q^54 - 20 * q^55 + 8 * q^57 - 140 * q^58 + 10 * q^60 + 164 * q^61 + 12 * q^63 - 82 * q^64 - 40 * q^66 + 48 * q^67 - 60 * q^69 - 60 * q^70 - 120 * q^72 - 148 * q^73 + 20 * q^75 + 4 * q^76 + 160 * q^78 + 276 * q^79 - 158 * q^81 + 280 * q^82 - 24 * q^84 - 20 * q^85 + 140 * q^87 + 60 * q^88 - 10 * q^90 - 192 * q^91 + 72 * q^93 - 220 * q^94 - 70 * q^96 - 332 * q^97 + 80 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(15, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.3.c.a	$15$	$3$	15.c	3.b	$2$	$2$	$2$	$0.409$	\(\Q(\sqrt{-5}) \)	None		✓	✓	✓	15.3.c.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots\)