Space of modular forms of level 14, weight 6, and Character 14.c

• Label: 14.6.c
• Level: $14$
• Weight: $6$
• Character orbit: 14.c
• Rep. character: $\chi_{14}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(14, [\chi])\).

	Total	New	Old
Modular forms	24	8	16
Cusp forms	16	8	8
Eisenstein series	8	0	8

Trace form

8 * q - 64 * q^4 - 28 * q^5 + 224 * q^6 + 232 * q^7 - 896 * q^9 - 448 * q^10 + 232 * q^11 + 3360 * q^13 + 272 * q^14 - 3488 * q^15 - 1024 * q^16 - 2996 * q^17 + 1632 * q^18 + 616 * q^19 + 896 * q^20 + 8692 * q^21 + 2848 * q^22 + 88 * q^23 - 1792 * q^24 - 944 * q^25 - 7840 * q^26 - 17136 * q^27 - 6656 * q^28 - 2368 * q^29 + 9328 * q^30 + 17472 * q^31 + 14924 * q^33 + 3136 * q^34 - 14504 * q^35 + 28672 * q^36 + 3964 * q^37 - 9072 * q^38 - 16328 * q^39 - 7168 * q^40 + 2016 * q^41 - 53856 * q^42 - 41120 * q^43 + 3712 * q^44 + 40544 * q^45 + 21520 * q^46 + 40320 * q^47 + 53768 * q^49 + 93440 * q^50 - 35368 * q^51 - 26880 * q^52 - 38964 * q^53 - 91504 * q^54 - 18704 * q^55 - 14848 * q^56 - 123624 * q^57 + 18080 * q^58 - 37744 * q^59 + 27904 * q^60 + 51660 * q^61 + 96992 * q^62 + 227256 * q^63 + 32768 * q^64 - 31248 * q^65 - 98560 * q^66 + 70640 * q^67 - 47936 * q^68 - 7336 * q^69 - 112784 * q^70 - 200864 * q^71 + 26112 * q^72 + 12068 * q^73 + 57312 * q^74 + 95200 * q^75 - 19712 * q^76 + 4172 * q^77 + 214784 * q^78 - 60792 * q^79 - 7168 * q^80 - 116108 * q^81 - 45024 * q^82 + 47488 * q^83 - 71360 * q^84 - 47336 * q^85 + 46080 * q^86 + 225736 * q^87 - 22784 * q^88 - 47628 * q^89 - 105280 * q^90 - 177552 * q^91 - 2816 * q^92 + 27892 * q^93 + 41328 * q^94 - 157784 * q^95 - 28672 * q^96 - 103936 * q^97 - 50016 * q^98 + 558832 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(14, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
14.6.c.a	$14$	$6$	14.c	7.c	$3$	$4$	$2$	$2.245$	\(\Q(\sqrt{-3}, \sqrt{79})\)	None		✓			14.6.c.a	$2$	$0$	\(-8\)	\(-14\)	\(-70\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\beta _{2}q^{2}+(-7-\beta _{1}-7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
14.6.c.b	$14$	$6$	14.c	7.c	$3$	$4$	$2$	$2.245$	\(\Q(\sqrt{-3}, \sqrt{130})\)	None		✓			14.6.c.b	$2$	$0$	\(8\)	\(14\)	\(42\)	\(232\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\beta _{2}q^{2}+(7-\beta _{1}+7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(14, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)