Space of modular forms of level 39, weight 5, and Character 39.c

• Label: 39.5.c
• Level: $39$
• Weight: $5$
• Character orbit: 39.c
• Rep. character: $\chi_{39}(14,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $23$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	39.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(23\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(39, [\chi])\).

	Total	New	Old
Modular forms	20	16	4
Cusp forms	16	16	0
Eisenstein series	4	0	4

Trace form

16 * q - 2 * q^3 - 100 * q^4 + 96 * q^6 - 80 * q^7 + 66 * q^9 + 240 * q^10 - 102 * q^12 - 356 * q^15 + 456 * q^16 - 388 * q^18 - 112 * q^19 + 472 * q^21 - 316 * q^22 - 624 * q^24 - 1428 * q^25 + 1540 * q^27 + 3584 * q^28 - 1714 * q^30 - 3368 * q^31 + 1852 * q^33 - 640 * q^34 + 3862 * q^36 + 2336 * q^37 - 6776 * q^40 - 4326 * q^42 + 2956 * q^43 - 88 * q^45 + 4664 * q^46 + 1534 * q^48 + 5492 * q^49 - 8950 * q^51 - 3380 * q^52 - 14232 * q^54 + 3392 * q^55 + 4272 * q^57 + 544 * q^58 + 24444 * q^60 - 13400 * q^61 + 3452 * q^63 + 1788 * q^64 + 9504 * q^66 + 25352 * q^67 - 21296 * q^69 - 21736 * q^70 + 1908 * q^72 - 13928 * q^73 + 4540 * q^75 - 1728 * q^76 + 1690 * q^78 - 25496 * q^79 + 8346 * q^81 + 44460 * q^82 - 14384 * q^84 - 5104 * q^85 + 9332 * q^87 + 11820 * q^88 - 20634 * q^90 + 676 * q^91 - 35376 * q^93 - 30040 * q^94 + 32992 * q^96 + 39728 * q^97 + 48492 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(39, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
39.5.c.a	$39$	$5$	39.c	3.b	$2$	$16$	$16$	$4.031$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	39.5.c.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-80\)	$2^{10}\cdot 3^{5}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-6+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)