Space of modular forms of level 14, weight 12, and Character 14.c

• Label: 14.12.c
• Level: $14$
• Weight: $12$
• Character orbit: 14.c
• Rep. character: $\chi_{14}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
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:			\(24\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(14, [\chi])\).

	Total	New	Old
Modular forms	48	16	32
Cusp forms	40	16	24
Eisenstein series	8	0	8

Trace form

16 * q - 8192 * q^4 + 11312 * q^5 - 34048 * q^6 + 68104 * q^7 - 627368 * q^9 + 118272 * q^10 + 1133176 * q^11 - 1612240 * q^13 + 2654336 * q^14 + 1775056 * q^15 - 8388608 * q^16 + 10187968 * q^17 + 12170496 * q^18 - 14318920 * q^19 - 23166976 * q^20 - 41167352 * q^21 + 45255936 * q^22 + 61861024 * q^23 + 17432576 * q^24 - 196562000 * q^25 + 57714944 * q^26 + 175695408 * q^27 - 65282048 * q^28 - 7839472 * q^29 - 44415104 * q^30 + 291871496 * q^31 + 325323992 * q^33 - 481313280 * q^34 - 1737885464 * q^35 + 1284849664 * q^36 + 634648088 * q^37 + 921105024 * q^38 - 159200840 * q^39 + 121110528 * q^40 - 4929818544 * q^41 - 2762479872 * q^42 + 3777176000 * q^43 + 1160372224 * q^44 + 9655050104 * q^45 - 2661097344 * q^46 + 1329789720 * q^47 - 15841003184 * q^49 + 2704160768 * q^50 + 13918649240 * q^51 + 825466880 * q^52 - 8634346872 * q^53 + 2202736256 * q^54 - 24498433344 * q^55 - 4998823936 * q^56 + 22974199632 * q^57 + 6959834880 * q^58 + 21384302240 * q^59 - 908828672 * q^60 + 4377938936 * q^61 - 43557826816 * q^62 - 29085810312 * q^63 + 17179869184 * q^64 + 36121112328 * q^65 + 20941383680 * q^66 + 968573360 * q^67 + 10432479232 * q^68 - 61447316896 * q^69 - 13888060032 * q^70 + 24699254176 * q^71 + 12462587904 * q^72 + 25151800184 * q^73 + 9331647744 * q^74 - 27465986576 * q^75 + 29325148160 * q^76 - 687714496 * q^77 - 73411176448 * q^78 - 48025080160 * q^79 + 11861491712 * q^80 + 3502213696 * q^81 - 27109947648 * q^82 + 176845941664 * q^83 + 56780701696 * q^84 - 38209307952 * q^85 - 33225867264 * q^86 - 295758917048 * q^87 - 23171039232 * q^88 + 55149699528 * q^89 + 250430620160 * q^90 + 233972705648 * q^91 - 126691377152 * q^92 - 204137018504 * q^93 - 99775111296 * q^94 + 153407449936 * q^95 + 17850957824 * q^96 + 150068913008 * q^97 + 347442899712 * q^98 - 152071856816 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(14, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
14.12.c.a	$14$	$12$	14.c	7.c	$3$	$8$	$4$	$10.757$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			14.12.c.a	$2$	$0$	\(-128\)	\(266\)	\(7504\)	\(-42224\)	$2^{12}\cdot 3\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2^{5}+2^{5}\beta _{2})q^{2}+(67\beta _{2}-\beta _{3})q^{3}+\cdots\)
14.12.c.b	$14$	$12$	14.c	7.c	$3$	$8$	$4$	$10.757$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			14.12.c.b	$2$	$0$	\(128\)	\(-266\)	\(3808\)	\(110328\)	$2^{12}\cdot 3\cdot 7^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+2^{5}\beta _{2}q^{2}+(-67+\beta _{1}+67\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(14, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)