Space of modular forms of level 3696, weight 2, and Character 3696.d

• Label: 3696.2.d
• Level: $3696$
• Weight: $2$
• Character orbit: 3696.d
• Rep. character: $\chi_{3696}(2575,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $1536$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3696.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1536\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3696, [\chi])\).

	Total	New	Old
Modular forms	792	80	712
Cusp forms	744	80	664
Eisenstein series	48	0	48

Trace form

\( 80 q + 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3696, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3696.2.d.a	$3696$	$2$	3696.d	28.d	$2$	$4$	$4$	$29.513$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{2})q^{7}+q^{9}+\cdots\)
3696.2.d.b	$3696$	$2$	3696.d	28.d	$2$	$4$	$4$	$29.513$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
3696.2.d.c	$3696$	$2$	3696.d	28.d	$2$	$8$	$8$	$29.513$	8.0.836829184.2	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(\beta _{1}-\beta _{4})q^{5}+(-1+\beta _{2}-\beta _{5}+\cdots)q^{7}+\cdots\)
3696.2.d.d	$3696$	$2$	3696.d	28.d	$2$	$8$	$8$	$29.513$	8.0.836829184.2	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(\beta _{1}-\beta _{4})q^{5}+(1-\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)
3696.2.d.e	$3696$	$2$	3696.d	28.d	$2$	$28$	$28$	$29.513$		None		$2$	$0$	\(0\)	\(-28\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$
3696.2.d.f	$3696$	$2$	3696.d	28.d	$2$	$28$	$28$	$29.513$		None		$2$	$0$	\(0\)	\(28\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3696, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \)