Space of modular forms of level 14, weight 4, and trivial character

• Label: 14.4.a
• Level: $14$
• Weight: $4$
• Character orbit: 14.a
• Rep. character: $\chi_{14}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $8$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(8\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(14))\).

	Total	New	Old
Modular forms	8	2	6
Cusp forms	4	2	2
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
\(+\)	\(+\)	\(+\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(1\)	\(0\)	\(1\)		\(0\)	\(0\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(2\)	\(1\)	\(1\)		\(1\)	\(1\)	\(0\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(5\)	\(2\)	\(3\)		\(3\)	\(2\)	\(1\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)		\(2\)	\(0\)	\(2\)

Trace form

2 * q + 6 * q^3 + 8 * q^4 - 26 * q^5 - 20 * q^6 + 14 * q^9 + 4 * q^10 + 20 * q^11 + 24 * q^12 + 74 * q^13 + 28 * q^14 - 88 * q^15 + 32 * q^16 - 40 * q^17 - 120 * q^18 + 82 * q^19 - 104 * q^20 - 70 * q^21 + 152 * q^22 - 232 * q^23 - 80 * q^24 + 90 * q^25 + 76 * q^26 + 180 * q^27 + 136 * q^29 + 272 * q^30 + 308 * q^31 - 320 * q^33 - 376 * q^34 + 14 * q^35 + 56 * q^36 - 200 * q^37 - 156 * q^38 + 32 * q^39 + 16 * q^40 + 288 * q^41 + 84 * q^42 - 788 * q^43 + 80 * q^44 - 242 * q^45 - 16 * q^46 + 12 * q^47 + 96 * q^48 + 98 * q^49 - 104 * q^50 + 820 * q^51 + 296 * q^52 + 492 * q^53 + 40 * q^54 - 184 * q^55 + 112 * q^56 + 636 * q^57 - 488 * q^58 - 62 * q^59 - 352 * q^60 + 182 * q^61 + 328 * q^62 - 420 * q^63 + 128 * q^64 - 924 * q^65 + 256 * q^66 - 1200 * q^67 - 160 * q^68 - 656 * q^69 - 364 * q^70 + 968 * q^71 - 480 * q^72 - 612 * q^73 + 984 * q^74 + 530 * q^75 + 328 * q^76 + 532 * q^77 - 512 * q^78 + 1016 * q^79 - 416 * q^80 + 62 * q^81 - 72 * q^82 - 694 * q^83 - 280 * q^84 + 332 * q^85 + 72 * q^86 + 1628 * q^87 + 608 * q^88 + 420 * q^89 + 1588 * q^90 + 266 * q^91 - 928 * q^92 + 104 * q^93 - 72 * q^94 - 1144 * q^95 - 320 * q^96 + 24 * q^97 - 2140 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.4.a.a	$14$	$4$	14.a	1.a	$1$	$1$	$1$	$0.826$	\(\Q\)	None	✓	✓	✓	✓	14.4.a.a	$1$	$0$	\(-2\)	\(8\)	\(-14\)	\(-7\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+8q^{3}+4q^{4}-14q^{5}-2^{4}q^{6}+\cdots\)
14.4.a.b	$14$	$4$	14.a	1.a	$1$	$1$	$1$	$0.826$	\(\Q\)	None	✓	✓	✓	✓	14.4.a.b	$1$	$0$	\(2\)	\(-2\)	\(-12\)	\(7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-2q^{3}+4q^{4}-12q^{5}-4q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

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