Space of modular forms of level 144, weight 12, and Character 144.c

• Label: 144.12.c
• Level: $144$
• Weight: $12$
• Character orbit: 144.c
• Rep. character: $\chi_{144}(143,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	144.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(144, [\chi])\).

	Total	New	Old
Modular forms	276	22	254
Cusp forms	252	22	230
Eisenstein series	24	0	24

Trace form

\( 22 q + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(144, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.12.c.a	$144$	$12$	144.c	12.b	$2$	$2$	$2$	$110.641$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		✓			144.12.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+3037\beta q^{5}-492092q^{13}+916607\beta q^{17}+\cdots\)
144.12.c.b	$144$	$12$	144.c	12.b	$2$	$4$	$4$	$110.641$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		✓			144.12.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+895\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{3}q^{11}+144892q^{13}+\cdots\)
144.12.c.c	$144$	$12$	144.c	12.b	$2$	$16$	$16$	$110.641$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		144.12.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{118}\cdot 3^{58}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{5}+\beta _{5}q^{7}+\beta _{9}q^{11}+(218272+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(144, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)