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

• Label: 144.7.e
• Level: $144$
• Weight: $7$
• Character orbit: 144.e
• Rep. character: $\chi_{144}(17,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $168$
• Trace bound: $7$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	156	12	144
Cusp forms	132	12	120
Eisenstein series	24	0	24

Trace form

\( 12 q + 720 q^{7} + O(q^{10}) \)

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.e.a	$144$	$7$	144.e	3.b	$2$	$2$	$2$	$33.128$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1048\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta q^{5}-524q^{7}+68\beta q^{11}+344q^{13}+\cdots\)
144.7.e.b	$144$	$7$	144.e	3.b	$2$	$2$	$2$	$33.128$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-120\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta q^{5}-60q^{7}-236\beta q^{11}+1192q^{13}+\cdots\)
144.7.e.c	$144$	$7$	144.e	3.b	$2$	$2$	$2$	$33.128$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(488\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta q^{5}+244q^{7}-188\beta q^{11}-2728q^{13}+\cdots\)
144.7.e.d	$144$	$7$	144.e	3.b	$2$	$2$	$2$	$33.128$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(968\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+41\beta q^{5}+22^{2}q^{7}-316\beta q^{11}+3368q^{13}+\cdots\)
144.7.e.e	$144$	$7$	144.e	3.b	$2$	$4$	$4$	$33.128$	\(\Q(\sqrt{-2}, \sqrt{145})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(432\)	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-5^{2}\beta _{1}-\beta _{3})q^{5}+(108+\beta _{2})q^{7}+\cdots\)

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

\( S_{7}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)