Space of modular forms of level 14, weight 7, and Character 14.d

• Label: 14.7.d
• Level: $14$
• Weight: $7$
• Character orbit: 14.d
• Rep. character: $\chi_{14}(3,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $14$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(14\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(14, [\chi])\).

	Total	New	Old
Modular forms	28	8	20
Cusp forms	20	8	12
Eisenstein series	8	0	8

Trace form

8 * q - 128 * q^4 - 336 * q^5 + 652 * q^7 + 756 * q^9 - 2016 * q^10 - 1356 * q^11 + 2064 * q^14 + 27144 * q^15 - 4096 * q^16 - 17304 * q^17 - 6816 * q^18 - 32004 * q^19 + 9756 * q^21 + 25248 * q^22 - 4128 * q^23 + 10752 * q^24 + 4664 * q^25 - 4704 * q^26 - 7552 * q^28 - 30312 * q^29 + 9648 * q^30 - 3108 * q^31 + 3276 * q^33 + 98028 * q^35 - 48384 * q^36 - 6124 * q^37 + 155568 * q^38 + 100764 * q^39 + 64512 * q^40 - 315936 * q^42 - 297376 * q^43 - 43392 * q^44 - 172116 * q^45 - 194064 * q^46 + 313908 * q^47 + 32432 * q^49 + 38784 * q^50 + 253692 * q^51 + 255360 * q^52 + 278484 * q^53 + 386064 * q^54 - 125952 * q^56 - 81288 * q^57 - 169824 * q^58 - 835464 * q^59 - 434304 * q^60 - 995316 * q^61 + 1216188 * q^63 + 262144 * q^64 + 8316 * q^65 + 1673280 * q^66 + 648808 * q^67 + 553728 * q^68 - 1572816 * q^70 + 190128 * q^71 - 218112 * q^72 - 1617084 * q^73 - 1158144 * q^74 - 2042208 * q^75 + 1456224 * q^77 + 1122432 * q^78 + 70096 * q^79 + 344064 * q^80 + 1177920 * q^81 + 66528 * q^82 - 1133568 * q^84 + 2190984 * q^85 - 573024 * q^86 - 2057076 * q^87 - 403968 * q^88 + 739116 * q^89 + 2233752 * q^91 + 264192 * q^92 - 23364 * q^93 + 3795120 * q^94 + 725640 * q^95 - 344064 * q^96 - 3532320 * q^98 - 4625928 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(14, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
14.7.d.a	$14$	$7$	14.d	7.d	$6$	$8$	$4$	$3.221$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓	✓	14.7.d.a	$2$	$0$	\(0\)	\(0\)	\(-336\)	\(652\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}-\beta _{3})q^{2}+(-\beta _{2}+2\beta _{3}-\beta _{6}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

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