Space of modular forms of level 14, weight 6, and trivial character

• Label: 14.6.a
• Level: $14$
• Weight: $6$
• Character orbit: 14.a
• Rep. character: $\chi_{14}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(14))\).

	Total	New	Old
Modular forms	12	2	10
Cusp forms	8	2	6
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
\(+\)	\(+\)	\(+\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(5\)	\(0\)	\(5\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(7\)	\(2\)	\(5\)		\(5\)	\(2\)	\(3\)		\(2\)	\(0\)	\(2\)

Trace form

2 * q + 18 * q^3 + 32 * q^4 + 94 * q^5 - 8 * q^6 - 322 * q^9 - 296 * q^10 - 676 * q^11 + 288 * q^12 + 290 * q^13 - 392 * q^14 + 920 * q^15 + 512 * q^16 - 232 * q^17 - 144 * q^18 + 2902 * q^19 + 1504 * q^20 + 98 * q^21 - 16 * q^22 - 2200 * q^23 - 128 * q^24 + 906 * q^25 - 3512 * q^26 - 7236 * q^27 - 1880 * q^29 - 3040 * q^30 + 1484 * q^31 - 6080 * q^33 + 10736 * q^34 + 3626 * q^35 - 5152 * q^36 + 23512 * q^37 + 7848 * q^38 + 3488 * q^39 - 4736 * q^40 - 8352 * q^41 - 3528 * q^42 + 11812 * q^43 - 10816 * q^44 - 13802 * q^45 + 24800 * q^46 - 2124 * q^47 + 4608 * q^48 + 4802 * q^49 - 27824 * q^50 - 4772 * q^51 + 4640 * q^52 - 51876 * q^53 + 1936 * q^54 - 31624 * q^55 - 6272 * q^56 + 24156 * q^57 - 46448 * q^58 + 6646 * q^59 + 14720 * q^60 + 58814 * q^61 + 64912 * q^62 + 1764 * q^63 + 8192 * q^64 + 46116 * q^65 + 2560 * q^66 - 5136 * q^67 - 3712 * q^68 - 26000 * q^69 - 18424 * q^70 + 65144 * q^71 - 2304 * q^72 - 58116 * q^73 - 20592 * q^74 + 15110 * q^75 + 46432 * q^76 + 196 * q^77 - 32768 * q^78 - 21880 * q^79 + 24064 * q^80 + 12638 * q^81 - 83184 * q^82 - 112258 * q^83 + 1568 * q^84 - 110212 * q^85 + 17616 * q^86 - 5308 * q^87 - 256 * q^88 + 18564 * q^89 + 40888 * q^90 + 43022 * q^91 - 35200 * q^92 - 2872 * q^93 + 6000 * q^94 + 63800 * q^95 - 2048 * q^96 + 3672 * q^97 + 108908 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.6.a.a	$14$	$6$	14.a	1.a	$1$	$1$	$1$	$2.245$	\(\Q\)	None	✓	✓	✓	✓	14.6.a.a	$1$	$0$	\(-4\)	\(10\)	\(84\)	\(49\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+10q^{3}+2^{4}q^{4}+84q^{5}-40q^{6}+\cdots\)
14.6.a.b	$14$	$6$	14.a	1.a	$1$	$1$	$1$	$2.245$	\(\Q\)	None	✓	✓	✓	✓	14.6.a.b	$1$	$0$	\(4\)	\(8\)	\(10\)	\(-49\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+8q^{3}+2^{4}q^{4}+10q^{5}+2^{5}q^{6}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(14)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)