Space of modular forms of level 14, weight 4, and Character 14.c

• Label: 14.4.c
• Level: $14$
• Weight: $4$
• Character orbit: 14.c
• Rep. character: $\chi_{14}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $8$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(8\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(14, [\chi])\).

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

Trace form

4 * q + 6 * q^3 - 8 * q^4 + 2 * q^5 - 16 * q^6 - 48 * q^7 + 28 * q^9 + 32 * q^10 + 22 * q^11 + 24 * q^12 - 8 * q^13 + 104 * q^14 + 76 * q^15 - 32 * q^16 - 110 * q^17 - 48 * q^18 - 142 * q^19 - 16 * q^20 - 2 * q^21 - 368 * q^22 - 62 * q^23 + 32 * q^24 + 120 * q^25 + 272 * q^26 + 396 * q^27 + 120 * q^28 + 440 * q^29 - 104 * q^30 - 98 * q^31 - 250 * q^33 - 32 * q^34 - 434 * q^35 - 224 * q^36 + 242 * q^37 + 264 * q^38 - 284 * q^39 + 128 * q^40 - 1080 * q^41 + 240 * q^42 + 272 * q^43 + 88 * q^44 + 164 * q^45 - 152 * q^46 - 30 * q^47 - 192 * q^48 - 188 * q^49 + 128 * q^50 + 314 * q^51 + 16 * q^52 + 810 * q^53 - 184 * q^54 + 1516 * q^55 - 64 * q^56 - 324 * q^57 - 16 * q^58 - 202 * q^59 - 152 * q^60 + 658 * q^61 - 208 * q^62 + 372 * q^63 + 256 * q^64 - 1092 * q^65 - 640 * q^66 - 858 * q^67 - 440 * q^68 - 676 * q^69 - 392 * q^70 - 1760 * q^71 - 192 * q^72 + 18 * q^73 + 528 * q^74 - 296 * q^75 + 1136 * q^76 + 1694 * q^77 + 1664 * q^78 + 34 * q^79 + 32 * q^80 + 22 * q^81 - 912 * q^82 + 688 * q^83 - 632 * q^84 - 92 * q^85 + 768 * q^86 + 676 * q^87 + 736 * q^88 + 1890 * q^89 + 800 * q^90 + 640 * q^91 + 496 * q^92 + 190 * q^93 - 744 * q^94 - 914 * q^95 + 128 * q^96 - 4248 * q^97 - 2640 * q^98 - 1592 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(14, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
14.4.c.a	$14$	$4$	14.c	7.c	$3$	$2$	$1$	$0.826$	\(\Q(\sqrt{-3}) \)	None		✓			14.4.c.a	$2$	$0$	\(-2\)	\(5\)	\(9\)	\(-28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
14.4.c.b	$14$	$4$	14.c	7.c	$3$	$2$	$1$	$0.826$	\(\Q(\sqrt{-3}) \)	None		✓			14.4.c.b	$2$	$0$	\(2\)	\(1\)	\(-7\)	\(-20\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(14, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)