Space of modular forms of level 12, weight 14, and trivial character

• Label: 12.14.a
• Level: $12$
• Weight: $14$
• Character orbit: 12.a
• Rep. character: $\chi_{12}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	12.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(28\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(12))\).

	Total	New	Old
Modular forms	29	2	27
Cusp forms	23	2	21
Eisenstein series	6	0	6

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

\(2\)	\(3\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(7\)	\(0\)	\(7\)		\(5\)	\(0\)	\(5\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(8\)	\(0\)	\(8\)		\(6\)	\(0\)	\(6\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(7\)	\(1\)	\(6\)		\(6\)	\(1\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(7\)	\(1\)	\(6\)		\(6\)	\(1\)	\(5\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(14\)	\(1\)	\(13\)		\(11\)	\(1\)	\(10\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(15\)	\(1\)	\(14\)		\(12\)	\(1\)	\(11\)		\(3\)	\(0\)	\(3\)

Trace form

2 * q - 39420 * q^5 - 236600 * q^7 + 1062882 * q^9 + 4134672 * q^11 - 12665300 * q^13 - 7085880 * q^15 - 37133100 * q^17 + 213076240 * q^19 - 80779032 * q^21 + 255949200 * q^23 - 1617198850 * q^25 + 3218470308 * q^29 + 1704049768 * q^31 - 4428675000 * q^33 + 5201912880 * q^35 - 13684978100 * q^37 - 25976836080 * q^39 + 78636484260 * q^41 - 42437954000 * q^43 - 20949404220 * q^45 + 145332500400 * q^47 - 159649034382 * q^49 - 201978757872 * q^51 + 326512768500 * q^53 - 51969885120 * q^55 - 329599708200 * q^57 + 797939131968 * q^59 - 394141653476 * q^61 - 125738940600 * q^63 + 422811970200 * q^65 - 1041137585600 * q^67 - 325060493472 * q^69 + 330977445840 * q^71 + 1172827143700 * q^73 + 279325389600 * q^75 - 152552397600 * q^77 + 1342025487496 * q^79 + 564859072962 * q^81 - 7513614010800 * q^83 + 2078418453480 * q^85 + 4913951491800 * q^87 - 7206989841900 * q^89 + 3472544532080 * q^91 + 6978351771000 * q^93 - 2002401302400 * q^95 + 2580877756900 * q^97 + 2197334222352 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(12))\) 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	3
12.14.a.a	$12$	$14$	12.a	1.a	$1$	$1$	$1$	$12.868$	\(\Q\)	None	✓	✓	✓	✓	12.14.a.a	$1$	$0$	\(0\)	\(-729\)	\(-14850\)	\(-62896\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}-14850q^{5}-62896q^{7}+\cdots\)
12.14.a.b	$12$	$14$	12.a	1.a	$1$	$1$	$1$	$12.868$	\(\Q\)	None	✓	✓	✓	✓	12.14.a.b	$1$	$1$	\(0\)	\(729\)	\(-24570\)	\(-173704\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}-24570q^{5}-173704q^{7}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(12)) \simeq \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)