Space of modular forms of level 5, weight 13, and Character 5.c

• Label: 5.13.c
• Level: $5$
• Weight: $13$
• Character orbit: 5.c
• Rep. character: $\chi_{5}(2,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 13 \)
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:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(5, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

Trace form

10 * q - 2 * q^2 + 318 * q^3 - 4250 * q^5 - 175080 * q^6 + 279598 * q^7 - 469980 * q^8 + 1552150 * q^10 + 312620 * q^11 - 2359992 * q^12 + 5290738 * q^13 - 5821650 * q^15 + 30547960 * q^16 - 41269502 * q^17 - 140573742 * q^18 + 334988100 * q^20 + 107493420 * q^21 - 155490544 * q^22 - 510099842 * q^23 + 942201250 * q^25 + 1475846420 * q^26 - 1993958640 * q^27 - 3562106488 * q^28 + 5922516000 * q^30 + 3077089820 * q^31 - 4623883832 * q^32 - 7503698004 * q^33 + 9330787150 * q^35 + 7760793660 * q^36 - 2599618502 * q^37 - 15310240920 * q^38 + 15901243500 * q^40 + 7412079020 * q^41 - 18593270064 * q^42 - 5784410402 * q^43 - 10510145100 * q^45 - 7382547880 * q^46 + 16053249598 * q^47 + 42572492208 * q^48 - 68314688750 * q^50 - 33139878180 * q^51 + 96763417228 * q^52 + 101763514618 * q^53 - 84180068500 * q^55 - 172002747600 * q^56 + 27733489920 * q^57 + 135238672320 * q^58 - 220124568600 * q^60 + 7731718220 * q^61 + 193287375176 * q^62 + 207465112158 * q^63 - 338075024150 * q^65 - 60815472960 * q^66 - 80010636002 * q^67 + 204699541412 * q^68 + 376969924200 * q^70 - 46557252580 * q^71 - 13986370620 * q^72 - 448527032342 * q^73 + 719724648750 * q^75 + 305095930800 * q^76 - 425580405844 * q^77 - 1690993241784 * q^78 + 873032236000 * q^80 + 1107831051810 * q^81 - 671946416464 * q^82 - 91118376722 * q^83 + 543768569650 * q^85 + 414117747320 * q^86 - 2078422804320 * q^87 - 1842434230560 * q^88 + 3098742811350 * q^90 + 2737742572220 * q^91 + 906853941448 * q^92 - 91295366484 * q^93 - 1044695070000 * q^95 - 3473259523680 * q^96 - 1409507601302 * q^97 - 1481746533298 * q^98

Decomposition of \(S_{13}^{\mathrm{new}}(5, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5.13.c.a	$5$	$13$	5.c	5.c	$4$	$10$	$5$	$4.570$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓	✓	5.13.c.a	$2$	$0$	\(-2\)	\(318\)	\(-4250\)	\(279598\)	$2^{13}\cdot 3^{2}\cdot 5^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{2}+(31-31\beta _{1}-\beta _{3}+3\beta _{6}+\cdots)q^{3}+\cdots\)