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

• Label: 13.10.e
• Level: $13$
• Weight: $10$
• Character orbit: 13.e
• Rep. character: $\chi_{13}(4,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $11$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$13$
Weight:	$k$	$=$	$10$
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:			$11$
Trace bound:			$0$

Dimensions

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

	Total	New	Old
Modular forms	24	24	0
Cusp forms	20	20	0
Eisenstein series	4	4	0

Trace form

20 * q - 3 * q^2 - 163 * q^3 + 2559 * q^4 - 3288 * q^6 + 1023 * q^7 - 64763 * q^9 + 44195 * q^10 - 94599 * q^11 - 427652 * q^12 + 187013 * q^13 + 473556 * q^14 + 754950 * q^15 - 594809 * q^16 - 49656 * q^17 - 3879 * q^19 - 154815 * q^20 + 2536766 * q^22 + 3126189 * q^23 - 6472626 * q^24 - 1529274 * q^25 - 13931889 * q^26 + 18052718 * q^27 + 4918980 * q^28 - 2712414 * q^29 + 15022758 * q^30 - 14390595 * q^32 - 34050309 * q^33 + 7549080 * q^35 + 27039443 * q^36 - 36102006 * q^37 - 39021096 * q^38 - 32365163 * q^39 + 134360674 * q^40 + 30265110 * q^41 - 60800034 * q^42 + 26621029 * q^43 + 31870857 * q^45 + 121485864 * q^46 - 41385538 * q^48 + 7027649 * q^49 - 58518456 * q^50 - 10208934 * q^51 - 109817238 * q^52 - 36429786 * q^53 - 393493974 * q^54 + 65727080 * q^55 + 63636336 * q^56 + 470295633 * q^58 + 3987867 * q^59 - 268212896 * q^61 - 445379898 * q^62 + 506780166 * q^63 + 343337066 * q^64 + 292006563 * q^65 - 445758060 * q^66 - 944780397 * q^67 - 168297045 * q^68 + 541942791 * q^69 + 1318764849 * q^71 + 1409393649 * q^72 - 541934631 * q^74 - 609413441 * q^75 - 594798654 * q^76 - 1470187374 * q^77 - 2076950874 * q^78 + 1556703616 * q^79 - 968911845 * q^80 - 1069563758 * q^81 + 1859661377 * q^82 + 7275171300 * q^84 - 318942363 * q^85 - 644123073 * q^87 - 2054580464 * q^88 - 2287100109 * q^89 - 6489878934 * q^90 - 4972612749 * q^91 + 10148843820 * q^92 - 1470324870 * q^93 - 2447356414 * q^94 + 4625601270 * q^95 + 7273214547 * q^97 - 1557570597 * q^98

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.e.a	$13$	$10$	13.e	13.e	$6$	$20$	$10$	$6.695$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	13.10.e.a	$2$	$0$	$-3$	$-163$	$0$	$1023$	$2^{22}\cdot 3^{10}\cdot 13^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{2})q^{2}+(2^{4}\beta _{5}-\beta _{6})q^{3}+(2^{8}+\cdots)q^{4}+\cdots$