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

• Label: 14.14.c
• Level: $14$
• Weight: $14$
• Character orbit: 14.c
• Rep. character: $\chi_{14}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
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:			\(28\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	56	16	40
Cusp forms	48	16	32
Eisenstein series	8	0	8

Trace form

16 * q - 32768 * q^4 - 62608 * q^5 + 46592 * q^6 - 382088 * q^7 - 3383912 * q^9 - 4236288 * q^10 - 9735704 * q^11 + 55245680 * q^13 + 50511104 * q^14 - 225762128 * q^15 - 134217728 * q^16 - 173276096 * q^17 - 293349888 * q^18 - 639112600 * q^19 + 512884736 * q^20 - 183034712 * q^21 - 987919872 * q^22 + 224305888 * q^23 - 95420416 * q^24 - 1799862224 * q^25 - 1675803136 * q^26 - 13674585456 * q^27 + 1788903424 * q^28 + 11874828752 * q^29 - 1535497472 * q^30 + 7620869816 * q^31 + 8347025624 * q^33 + 20145914880 * q^34 + 37241892856 * q^35 + 27721007104 * q^36 - 22905358216 * q^37 - 13292735232 * q^38 + 12213789640 * q^39 - 17351835648 * q^40 + 200030490576 * q^41 + 41592359424 * q^42 - 200631743680 * q^43 - 39877443584 * q^44 - 224768920936 * q^45 + 22282358016 * q^46 - 84492403800 * q^47 + 90125959504 * q^49 - 109545902080 * q^50 - 226281443320 * q^51 - 113143152640 * q^52 + 237123627816 * q^53 + 228393530624 * q^54 + 876549420096 * q^55 + 40531656704 * q^56 - 1935534418224 * q^57 - 784848668160 * q^58 - 1060437579040 * q^59 + 462360838144 * q^60 - 302092281064 * q^61 + 589655209472 * q^62 + 4198235629896 * q^63 + 1099511627776 * q^64 - 2789615117688 * q^65 - 2695993323520 * q^66 + 1651685797520 * q^67 - 709738889216 * q^68 + 9547459848416 * q^69 + 4454335286016 * q^70 - 2636562006944 * q^71 - 1201561141248 * q^72 - 6459088113352 * q^73 - 960899357184 * q^74 - 3701297994800 * q^75 + 5235610419200 * q^76 + 13324767549632 * q^77 - 7591038447616 * q^78 - 7522339758880 * q^79 - 1050387939328 * q^80 + 2466709187776 * q^81 - 872746581504 * q^82 + 3647678607328 * q^83 + 143615524864 * q^84 - 16115442141936 * q^85 - 560528154624 * q^86 - 14980266985544 * q^87 + 2023259897856 * q^88 + 1552477239432 * q^89 + 1899518028800 * q^90 + 4632739903568 * q^91 - 1837513834496 * q^92 - 17584118617448 * q^93 - 5005439894784 * q^94 + 15813845642416 * q^95 - 390842023936 * q^96 + 9790396414064 * q^97 - 2608265565696 * q^98 - 1131414590864 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(14, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
14.14.c.a	$14$	$14$	14.c	7.c	$3$	$8$	$4$	$15.012$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			14.14.c.a	$2$	$0$	\(-256\)	\(-182\)	\(-64400\)	\(-113736\)	$2^{14}\cdot 3\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2^{6}-2^{6}\beta _{1})q^{2}+(45\beta _{1}+\beta _{4})q^{3}+\cdots\)
14.14.c.b	$14$	$14$	14.c	7.c	$3$	$8$	$4$	$15.012$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			14.14.c.b	$2$	$0$	\(256\)	\(182\)	\(1792\)	\(-268352\)	$2^{14}\cdot 3\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{6}+2^{6}\beta _{1})q^{2}+(-46\beta _{1}-\beta _{2})q^{3}+\cdots\)

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

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