Space of modular forms of level 14, weight 5, and Character 14.d

• Label: 14.5.d
• Level: $14$
• Weight: $5$
• Character orbit: 14.d
• Rep. character: $\chi_{14}(3,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(14, [\chi])\).

	Total	New	Old
Modular forms	20	4	16
Cusp forms	12	4	8
Eisenstein series	8	0	8

Trace form

4 * q - 18 * q^3 - 16 * q^4 + 54 * q^5 - 28 * q^7 + 84 * q^9 - 96 * q^10 - 54 * q^11 + 144 * q^12 - 708 * q^15 - 128 * q^16 + 918 * q^17 + 576 * q^18 + 30 * q^19 - 378 * q^21 + 192 * q^22 - 486 * q^23 - 768 * q^24 - 572 * q^25 - 1728 * q^26 + 1456 * q^28 + 3240 * q^29 + 1152 * q^30 - 546 * q^31 + 1062 * q^33 - 1890 * q^35 - 1344 * q^36 - 446 * q^37 - 4320 * q^38 - 3312 * q^39 + 768 * q^40 + 5376 * q^42 + 2344 * q^43 - 432 * q^44 + 5724 * q^45 + 3840 * q^46 + 702 * q^47 - 9212 * q^49 - 3456 * q^50 + 318 * q^51 - 384 * q^52 + 2754 * q^53 - 1440 * q^54 - 17460 * q^57 + 384 * q^58 + 12366 * q^59 + 2832 * q^60 + 7686 * q^61 + 6468 * q^63 + 2048 * q^64 - 3024 * q^65 - 3456 * q^66 - 5062 * q^67 - 7344 * q^68 - 2016 * q^70 + 18792 * q^71 + 4608 * q^72 - 17274 * q^73 - 4320 * q^74 - 5220 * q^75 + 4914 * q^77 + 8832 * q^78 + 794 * q^79 - 3456 * q^80 - 4338 * q^81 + 9984 * q^82 - 5040 * q^84 + 10380 * q^85 - 10368 * q^86 - 12276 * q^87 - 768 * q^88 - 12474 * q^89 + 2688 * q^91 + 7776 * q^92 + 18918 * q^93 + 15168 * q^94 + 8910 * q^95 + 6144 * q^96 - 11448 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(14, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
14.5.d.a	$14$	$5$	14.d	7.d	$6$	$4$	$2$	$1.447$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓	✓	✓	14.5.d.a	$2$	$0$	\(0\)	\(-18\)	\(54\)	\(-28\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-6+2\beta _{1}-3\beta _{2}-2\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(14, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)