Space of modular forms of level 13, weight 14, and Character 13.e

• Label: 13.14.e
• Level: $13$
• Weight: $14$
• Character orbit: 13.e
• Rep. character: $\chi_{13}(4,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $30$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	13.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(13, [\chi])\).

	Total	New	Old
Modular forms	34	34	0
Cusp forms	30	30	0
Eisenstein series	4	4	0

Trace form

30 * q - 3 * q^2 - 730 * q^3 + 65535 * q^4 - 382584 * q^6 + 438984 * q^7 - 9117071 * q^9 + 3893475 * q^10 - 5364528 * q^11 + 27694876 * q^12 - 1794135 * q^13 + 61125588 * q^14 - 113380170 * q^15 - 350182521 * q^16 - 23524899 * q^17 + 92116746 * q^19 + 959687745 * q^20 - 128185362 * q^22 + 417086886 * q^23 - 4232784354 * q^24 - 11926991364 * q^25 + 5442553119 * q^26 + 5605403288 * q^27 + 22569369732 * q^28 - 8810189577 * q^29 - 9936679242 * q^30 + 9137241117 * q^32 + 12085621392 * q^33 + 1059240720 * q^35 + 55900963715 * q^36 - 72651649419 * q^37 - 45168847944 * q^38 - 41492436530 * q^39 + 137282090274 * q^40 - 3909896103 * q^41 - 34124964786 * q^42 + 138326640480 * q^43 - 259122942393 * q^45 - 288578831832 * q^46 + 630595691198 * q^48 + 114277635303 * q^49 - 553717814136 * q^50 - 178343342508 * q^51 - 1243882821894 * q^52 + 938994404670 * q^53 + 1180281528282 * q^54 - 140610123120 * q^55 + 932974200720 * q^56 - 768032047215 * q^58 - 1420851272556 * q^59 + 284498233437 * q^61 + 2574083847030 * q^62 - 3219361289664 * q^63 - 4989806279958 * q^64 - 931161533727 * q^65 + 12037245084948 * q^66 + 2624227676622 * q^67 - 3124046642277 * q^68 + 1206986427996 * q^69 - 1317657850698 * q^71 - 2571404508735 * q^72 + 1723434230073 * q^74 + 1909848151684 * q^75 - 5741418039246 * q^76 - 8153714196816 * q^77 - 13064083856250 * q^78 + 10732970056200 * q^79 + 11699811454875 * q^80 + 26873856445 * q^81 - 924448017327 * q^82 + 5758359493380 * q^84 - 14711656818213 * q^85 - 6442966126134 * q^87 - 11094606812688 * q^88 + 18293004024660 * q^89 + 53932182551466 * q^90 + 2271787574784 * q^91 - 48706576133844 * q^92 - 50634402753492 * q^93 + 3529466920146 * q^94 + 11308314514950 * q^95 - 4972913690148 * q^97 + 86959564160763 * q^98

Decomposition of \(S_{14}^{\mathrm{new}}(13, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
13.14.e.a	$13$	$14$	13.e	13.e	$6$	$30$	$15$	$13.940$		None		✓	✓	✓	13.14.e.a	$2$	$0$	\(-3\)	\(-730\)	\(0\)	\(438984\)		$\mathrm{SU}(2)[C_{6}]$