Space of modular forms of level 14, weight 16, and trivial character

• Label: 14.16.a
• Level: $14$
• Weight: $16$
• Character orbit: 14.a
• Rep. character: $\chi_{14}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(32\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(14))\).

	Total	New	Old
Modular forms	32	8	24
Cusp forms	28	8	20
Eisenstein series	4	0	4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(7\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(9\)	\(2\)	\(7\)		\(8\)	\(2\)	\(6\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(7\)	\(1\)	\(6\)		\(6\)	\(1\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(8\)	\(2\)	\(6\)		\(7\)	\(2\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(8\)	\(3\)	\(5\)		\(7\)	\(3\)	\(4\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(17\)	\(5\)	\(12\)		\(15\)	\(5\)	\(10\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(15\)	\(3\)	\(12\)		\(13\)	\(3\)	\(10\)		\(2\)	\(0\)	\(2\)

Trace form

8 * q + 256 * q^2 - 8130 * q^3 + 131072 * q^4 - 25926 * q^5 - 185600 * q^6 + 4194304 * q^8 + 15306476 * q^9 + 37406464 * q^10 + 22651932 * q^11 - 133201920 * q^12 - 351841858 * q^13 + 210827008 * q^14 - 280251208 * q^15 + 2147483648 * q^16 - 732728268 * q^17 + 9610596096 * q^18 - 11628612038 * q^19 - 424771584 * q^20 + 13550576522 * q^21 + 10492416512 * q^22 + 19052477880 * q^23 - 3040870400 * q^24 + 133541322180 * q^25 - 13699450624 * q^26 + 17152537716 * q^27 + 37244220684 * q^29 - 114663083008 * q^30 + 49216127012 * q^31 + 68719476736 * q^32 + 1223151148816 * q^33 - 194994549760 * q^34 - 189729483426 * q^35 + 250781302784 * q^36 - 623389364948 * q^37 + 90195355904 * q^38 - 1283475734704 * q^39 + 612867506176 * q^40 - 4617723051684 * q^41 + 461078666496 * q^42 - 2718570441644 * q^43 + 371129253888 * q^44 + 4972004158978 * q^45 + 1199523550208 * q^46 - 14176898095620 * q^47 - 2182380257280 * q^48 + 5425784582792 * q^49 - 3487705819904 * q^50 + 6318498765604 * q^51 - 5764577001472 * q^52 + 10311567439296 * q^53 - 15761003781632 * q^54 + 5241115548296 * q^55 + 3454189699072 * q^56 + 30418034645148 * q^57 + 8384613809152 * q^58 - 11249706779526 * q^59 - 4591635791872 * q^60 - 16868999086054 * q^61 + 14764167918080 * q^62 + 140242784556 * q^63 + 35184372088832 * q^64 + 112667788253916 * q^65 + 59116108257280 * q^66 + 83707932210024 * q^67 - 12005019942912 * q^68 - 60881399817152 * q^69 - 23644881428224 * q^70 - 291504937736184 * q^71 + 157460006436864 * q^72 + 267628193084328 * q^73 + 200996330046464 * q^74 - 859650232817590 * q^75 - 190523179630592 * q^76 + 203037091703796 * q^77 - 417829807529984 * q^78 + 204144141980360 * q^79 - 6959457632256 * q^80 + 1258211420958932 * q^81 - 962336312174592 * q^82 - 456972975850110 * q^83 + 222012645736448 * q^84 - 841608962840428 * q^85 + 200789926776320 * q^86 + 720803618326220 * q^87 + 171907752132608 * q^88 - 2110704983009808 * q^89 + 484333674988288 * q^90 + 932507600003882 * q^91 + 312155797585920 * q^92 + 461803859335880 * q^93 - 68123166159360 * q^94 + 1253520098241816 * q^95 - 49821620633600 * q^96 - 1169857172772396 * q^97 + 173625106649344 * q^98 - 1512609592308532 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(14))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7
14.16.a.a	$14$	$16$	14.a	1.a	$1$	$1$	$1$	$19.977$	\(\Q\)	None	✓	✓	✓	✓	14.16.a.a	$1$	$1$	\(-128\)	\(1350\)	\(-81060\)	\(823543\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}+1350q^{3}+2^{14}q^{4}-81060q^{5}+\cdots\)
14.16.a.b	$14$	$16$	14.a	1.a	$1$	$2$	$2$	$19.977$	\(\Q(\sqrt{169009}) \)	None	✓	✓	✓	✓	14.16.a.b	$1$	$0$	\(-256\)	\(-4690\)	\(-78022\)	\(-1647086\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}+(-2345-\beta )q^{3}+2^{14}q^{4}+\cdots\)
14.16.a.c	$14$	$16$	14.a	1.a	$1$	$2$	$2$	$19.977$	\(\Q(\sqrt{54961}) \)	None	✓	✓	✓	✓	14.16.a.c	$1$	$1$	\(256\)	\(-7602\)	\(180250\)	\(-1647086\)		$-$	$+$	$-$	$2\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{7}q^{2}+(-3801-\beta )q^{3}+2^{14}q^{4}+\cdots\)
14.16.a.d	$14$	$16$	14.a	1.a	$1$	$3$	$3$	$19.977$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	14.16.a.d	$1$	$0$	\(384\)	\(2812\)	\(-47094\)	\(2470629\)		$-$	$-$	$+$	$2^{4}\cdot 3\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+2^{7}q^{2}+(937+\beta _{1})q^{3}+2^{14}q^{4}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(14)) \simeq \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)