Space of modular forms of level 756, weight 2, and Character 756.l

• Label: 756.2.l
• Level: $756$
• Weight: $2$
• Character orbit: 756.l
• Rep. character: $\chi_{756}(289,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).

	Total	New	Old
Modular forms	324	16	308
Cusp forms	252	16	236
Eisenstein series	72	0	72

Trace form

\( 16 q - 8 q^{5} + q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(756, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
756.2.l.a	$756$	$2$	756.l	63.g	$3$	$2$	$1$	$6.037$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2q^{5}+(3-2\zeta_{6})q^{7}-4q^{11}+(-3+\cdots)q^{13}+\cdots\)
756.2.l.b	$756$	$2$	756.l	63.g	$3$	$14$	$7$	$6.037$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-3\)	$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{3}-\beta _{7})q^{5}-\beta _{5}q^{7}+(\beta _{9}-\beta _{13})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(756, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)