Space of modular forms of level 14, weight 8, and Character 14.c

• Label: 14.8.c
• Level: $14$
• Weight: $8$
• Character orbit: 14.c
• Rep. character: $\chi_{14}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(16\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(14, [\chi])\).

	Total	New	Old
Modular forms	32	8	24
Cusp forms	24	8	16
Eisenstein series	8	0	8

Trace form

8 * q - 256 * q^4 + 252 * q^5 - 1792 * q^6 - 1680 * q^7 - 1064 * q^9 + 1792 * q^10 - 8256 * q^11 + 24080 * q^13 - 24192 * q^14 + 46576 * q^15 - 16384 * q^16 + 82740 * q^17 - 23040 * q^18 + 43456 * q^19 - 32256 * q^20 - 261884 * q^21 + 55040 * q^22 + 111000 * q^23 + 57344 * q^24 - 107040 * q^25 + 75264 * q^26 - 483840 * q^27 - 53760 * q^28 + 154320 * q^29 + 232576 * q^30 + 236264 * q^31 - 282100 * q^33 - 200704 * q^34 + 129696 * q^35 + 136192 * q^36 + 647980 * q^37 + 309120 * q^38 + 589552 * q^39 + 114688 * q^40 - 700560 * q^41 + 1021440 * q^42 + 651040 * q^43 - 528384 * q^44 - 1794856 * q^45 - 98944 * q^46 - 357000 * q^47 + 367304 * q^49 - 5194752 * q^50 - 2238832 * q^51 - 770560 * q^52 + 43980 * q^53 + 1269632 * q^54 + 10240496 * q^55 + 1032192 * q^56 + 1399800 * q^57 - 2147840 * q^58 - 2502864 * q^59 - 1490432 * q^60 - 2741284 * q^61 + 1532160 * q^62 - 2635920 * q^63 + 2097152 * q^64 - 2810472 * q^65 + 5411840 * q^66 + 3905760 * q^67 + 5295360 * q^68 - 3498712 * q^69 + 9984128 * q^70 + 7749120 * q^71 - 1474560 * q^72 - 2914380 * q^73 - 3773184 * q^74 - 10993136 * q^75 - 5562368 * q^76 - 14111580 * q^77 - 21713920 * q^78 + 17866568 * q^79 + 1032192 * q^80 - 1833716 * q^81 + 15697920 * q^82 - 21245280 * q^83 + 8409856 * q^84 + 24930008 * q^85 + 1683456 * q^86 + 234640 * q^87 - 1761280 * q^88 - 10716300 * q^89 - 19102720 * q^90 - 33681760 * q^91 - 14208000 * q^92 + 21387220 * q^93 + 25452672 * q^94 + 19023576 * q^95 + 3670016 * q^96 + 8250480 * q^97 + 24837120 * q^98 + 59220736 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(14, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
14.8.c.a	$14$	$8$	14.c	7.c	$3$	$4$	$2$	$4.373$	\(\Q(\sqrt{-3}, \sqrt{2389})\)	None		✓			14.8.c.a	$2$	$0$	\(-16\)	\(56\)	\(238\)	\(168\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-8+8\beta _{1})q^{2}+(28\beta _{1}-\beta _{2})q^{3}+\cdots\)
14.8.c.b	$14$	$8$	14.c	7.c	$3$	$4$	$2$	$4.373$	\(\Q(\sqrt{-3}, \sqrt{949})\)	None		✓			14.8.c.b	$2$	$0$	\(16\)	\(-56\)	\(14\)	\(-1848\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+8\beta _{1}q^{2}+(-28+28\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(14, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)