Space of modular forms of level 144, weight 7, and Character 144.g

• Label: 144.7.g
• Level: $144$
• Weight: $7$
• Character orbit: 144.g
• Rep. character: $\chi_{144}(127,\cdot)$
• Character field: $\Q$
• Dimension: $15$
• Newform subspaces: $7$
• Sturm bound: $168$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	144.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(168\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(144, [\chi])\).

	Total	New	Old
Modular forms	156	15	141
Cusp forms	132	15	117
Eisenstein series	24	0	24

Trace form

\( 15 q - 66 q^{5} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.7.g.a	$144$	$7$	144.g	4.b	$2$	$1$	$1$	$33.128$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-234\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-234q^{5}-4070q^{13}+990q^{17}+\cdots\)
144.7.g.b	$144$	$7$	144.g	4.b	$2$	$2$	$2$	$33.128$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-300\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-150q^{5}+47\zeta_{6}q^{7}+213\zeta_{6}q^{11}+\cdots\)
144.7.g.c	$144$	$7$	144.g	4.b	$2$	$2$	$2$	$33.128$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-6q^{5}-29\zeta_{6}q^{7}+93\zeta_{6}q^{11}-2654q^{13}+\cdots\)
144.7.g.d	$144$	$7$	144.g	4.b	$2$	$2$	$2$	$33.128$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}\cdot 5$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{6}q^{7}-506q^{13}-14\zeta_{6}q^{19}-5^{6}q^{25}+\cdots\)
144.7.g.e	$144$	$7$	144.g	4.b	$2$	$2$	$2$	$33.128$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(180\)	\(0\)	$2^{3}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+90q^{5}+\zeta_{6}q^{7}-9\zeta_{6}q^{11}+1762q^{13}+\cdots\)
144.7.g.f	$144$	$7$	144.g	4.b	$2$	$2$	$2$	$33.128$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(300\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+150q^{5}-22\zeta_{6}q^{7}-33\zeta_{6}q^{11}+\cdots\)
144.7.g.g	$144$	$7$	144.g	4.b	$2$	$4$	$4$	$33.128$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{3}q^{11}+262q^{13}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)