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

• Label: 756.2.b
• Level: $756$
• Weight: $2$
• Character orbit: 756.b
• Rep. character: $\chi_{756}(55,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(5\), \(19\), \(47\)

Dimensions

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

	Total	New	Old
Modular forms	156	64	92
Cusp forms	132	64	68
Eisenstein series	24	0	24

Trace form

\( 64 q + O(q^{10}) \)

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.b.a	$756$	$2$	756.b	28.d	$2$	$4$	$4$	$6.037$	\(\Q(\sqrt{-2}, \sqrt{7})\)	\(\Q(\sqrt{-21}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{7}+\cdots\)
756.2.b.b	$756$	$2$	756.b	28.d	$2$	$4$	$4$	$6.037$	\(\Q(\sqrt{-2}, \sqrt{7})\)	\(\Q(\sqrt{-21}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
756.2.b.c	$756$	$2$	756.b	28.d	$2$	$12$	$12$	$6.037$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+(1+\beta _{11})q^{4}-\beta _{8}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
756.2.b.d	$756$	$2$	756.b	28.d	$2$	$12$	$12$	$6.037$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots\)
756.2.b.e	$756$	$2$	756.b	28.d	$2$	$16$	$16$	$6.037$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{11}q^{5}+\beta _{6}q^{7}+\cdots\)
756.2.b.f	$756$	$2$	756.b	28.d	$2$	$16$	$16$	$6.037$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{14}q^{2}+\beta _{8}q^{4}+\beta _{10}q^{5}+\beta _{6}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \)