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

• Label: 3696.2.t
• Level: $3696$
• Weight: $2$
• Character orbit: 3696.t
• Rep. character: $\chi_{3696}(2815,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $1536$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3696.t (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1536\)
Trace bound:			\(7\)
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	72	720
Cusp forms	744	72	672
Eisenstein series	48	0	48

Trace form

\( 72 q - 72 q^{9} + O(q^{10}) \)

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.t.a	$3696$	$2$	3696.t	44.c	$2$	$12$	$12$	$29.513$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{2}q^{5}-q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)
3696.2.t.b	$3696$	$2$	3696.t	44.c	$2$	$12$	$12$	$29.513$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{2}q^{5}+q^{7}-q^{9}+(1+\beta _{4}+\cdots)q^{11}+\cdots\)
3696.2.t.c	$3696$	$2$	3696.t	44.c	$2$	$24$	$24$	$29.513$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{2}]$
3696.2.t.d	$3696$	$2$	3696.t	44.c	$2$	$24$	$24$	$29.513$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(24\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1232, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1848, [\chi])\)\(^{\oplus 2}\)