Space of modular forms of level 13, weight 10, and Character 13.c

• Label: 13.10.c
• Level: $13$
• Weight: $10$
• Character orbit: 13.c
• Rep. character: $\chi_{13}(3,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $18$
• Newform subspaces: $1$
• Sturm bound: $11$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$13$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	13.c (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$13$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$1$
Sturm bound:			$11$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{10}(13, [\chi])$.

	Total	New	Old
Modular forms	22	22	0
Cusp forms	18	18	0
Eisenstein series	4	4	0

Trace form

18 * q + 15 * q^2 + 161 * q^3 - 1793 * q^4 - 2280 * q^5 + 2118 * q^6 - 1939 * q^7 - 14478 * q^8 - 33654 * q^9 + 46923 * q^10 - 5433 * q^11 + 8712 * q^12 - 212524 * q^13 - 9900 * q^14 - 347428 * q^15 + 400127 * q^16 + 248589 * q^17 - 38738 * q^18 - 311001 * q^19 + 927069 * q^20 + 1553030 * q^21 + 1857242 * q^22 + 591609 * q^23 - 4492800 * q^24 + 7008998 * q^25 - 3801525 * q^26 - 11603482 * q^27 + 2697168 * q^28 + 11014155 * q^29 - 6597836 * q^30 - 23148076 * q^31 - 11868417 * q^32 + 14131427 * q^33 + 21859862 * q^34 + 21112794 * q^35 + 10792871 * q^36 - 29215749 * q^37 + 14572188 * q^38 - 71569875 * q^39 + 27322222 * q^40 + 3328377 * q^41 + 39828306 * q^42 + 6074381 * q^43 + 31824624 * q^44 + 32857342 * q^45 + 36693338 * q^46 - 45575052 * q^47 - 30270064 * q^48 + 10293266 * q^49 - 49601730 * q^50 - 136587494 * q^51 - 35278230 * q^52 - 29480016 * q^53 + 152965386 * q^54 - 18710998 * q^55 - 7665444 * q^56 + 523363230 * q^57 - 163479359 * q^58 - 32715855 * q^59 - 188638416 * q^60 - 220502845 * q^61 - 59980476 * q^62 + 166572574 * q^63 - 924604030 * q^64 + 128091756 * q^65 - 48128076 * q^66 + 112659045 * q^67 - 238942419 * q^68 + 86003951 * q^69 + 2040150992 * q^70 - 236450709 * q^71 + 995206683 * q^72 - 211881220 * q^73 - 455580507 * q^74 + 968954813 * q^75 - 365789708 * q^76 - 2399230890 * q^77 - 441111970 * q^78 - 817519096 * q^79 + 580424625 * q^80 + 176914851 * q^81 + 941792217 * q^82 + 2225691456 * q^83 - 1819004068 * q^84 + 1812284636 * q^85 + 291320076 * q^86 + 69564799 * q^87 + 3178375740 * q^88 - 1154379039 * q^89 - 10225809510 * q^90 - 1658338903 * q^91 - 4545506592 * q^92 + 3136878060 * q^93 + 2755131560 * q^94 + 1779441012 * q^95 + 5906965568 * q^96 - 3616470111 * q^97 + 8263323501 * q^98 + 2262149268 * q^99

Decomposition of $S_{10}^{\mathrm{new}}(13, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
13.10.c.a	$13$	$10$	13.c	13.c	$3$	$18$	$9$	$6.695$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓	✓	13.10.c.a	$2$	$0$	$15$	$161$	$-2280$	$-1939$	$2^{16}\cdot 3^{3}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2\beta _{2}-\beta _{3})q^{2}+(-18\beta _{2}-\beta _{6}+\cdots)q^{3}+\cdots$