Space of modular forms of level 12, weight 18, and trivial character

• Label: 12.18.a
• Level: $12$
• Weight: $18$
• Character orbit: 12.a
• Rep. character: $\chi_{12}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	12.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(12))\).

	Total	New	Old
Modular forms	37	2	35
Cusp forms	31	2	29
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
\(+\)	\(+\)	\(+\)		\(9\)	\(0\)	\(9\)		\(7\)	\(0\)	\(7\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(10\)	\(0\)	\(10\)		\(8\)	\(0\)	\(8\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(9\)	\(1\)	\(8\)		\(8\)	\(1\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(9\)	\(1\)	\(8\)		\(8\)	\(1\)	\(7\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(18\)	\(1\)	\(17\)		\(15\)	\(1\)	\(14\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(19\)	\(1\)	\(18\)		\(16\)	\(1\)	\(15\)		\(3\)	\(0\)	\(3\)

Trace form

2 * q - 1477980 * q^5 - 24263960 * q^7 + 86093442 * q^9 - 1032380208 * q^11 - 874027700 * q^13 + 11415352680 * q^15 + 43735163220 * q^17 - 153568558640 * q^19 - 35623553112 * q^21 - 80527437360 * q^23 + 1079924741150 * q^25 - 2282551050492 * q^29 + 2168009129608 * q^31 - 4320806648760 * q^33 + 13207404535920 * q^35 - 38816475554900 * q^37 + 28716563238480 * q^39 + 17740604240100 * q^41 + 97730802970480 * q^43 - 63622192703580 * q^45 - 172678557920400 * q^47 - 156150915890382 * q^49 - 287565080446512 * q^51 + 1087043089943700 * q^53 + 190011694259520 * q^55 + 259956087018840 * q^57 - 182503267515072 * q^59 - 2937122125020356 * q^61 - 1044483916475160 * q^63 + 4453501300162200 * q^65 - 669199133977280 * q^67 - 4345109590241952 * q^69 + 12010628577638160 * q^71 - 1309673501636780 * q^73 - 16871662953986400 * q^75 + 14312669809183200 * q^77 - 12372197413768664 * q^79 + 3706040377703682 * q^81 + 43379661699213840 * q^83 - 70448847823448280 * q^85 - 33328475346849480 * q^87 + 98415339645711060 * q^89 - 1278589146387280 * q^91 - 86131414373528520 * q^93 + 147953880687427200 * q^95 - 9941979634166300 * q^97 - 44440582779697968 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(12))\) 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
12.18.a.a	$12$	$18$	12.a	1.a	$1$	$1$	$1$	$21.987$	\(\Q\)	None	✓	✓	✓	✓	12.18.a.a	$1$	$0$	\(0\)	\(-6561\)	\(-1608930\)	\(-9417184\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{8}q^{3}-1608930q^{5}-9417184q^{7}+\cdots\)
12.18.a.b	$12$	$18$	12.a	1.a	$1$	$1$	$1$	$21.987$	\(\Q\)	None	✓	✓	✓	✓	12.18.a.b	$1$	$1$	\(0\)	\(6561\)	\(130950\)	\(-14846776\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{8}q^{3}+130950q^{5}-14846776q^{7}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(12)) \simeq \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)