Space of modular forms of level 6624, weight 2, and Character 6624.b

• Label: 6624.2.b
• Level: $6624$
• Weight: $2$
• Character orbit: 6624.b
• Rep. character: $\chi_{6624}(2897,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $3$
• Sturm bound: $2304$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 6624 = 2^{5} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6624.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 552 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(2304\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6624, [\chi])\).

	Total	New	Old
Modular forms	1184	96	1088
Cusp forms	1120	96	1024
Eisenstein series	64	0	64

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6624, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6624.2.b.a	$6624$	$2$	6624.b	552.b	$2$	$8$	$8$	$52.893$	8.0.\(\cdots\).17	\(\Q(\sqrt{-46}) \)					1656.2.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{5}q^{5}+(-\beta _{5}+2\beta _{6})q^{11}+\beta _{2}q^{19}+\cdots\)
6624.2.b.b	$6624$	$2$	6624.b	552.b	$2$	$8$	$8$	$52.893$	8.0.\(\cdots\).17	\(\Q(\sqrt{-46}) \)					1656.2.b.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{4}q^{5}-\beta _{4}q^{11}+(-\beta _{5}+\beta _{6})q^{19}+\cdots\)
6624.2.b.c	$6624$	$2$	6624.b	552.b	$2$	$80$	$80$	$52.893$		None			✓		1656.2.b.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(6624, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6624, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1656, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3312, [\chi])\)\(^{\oplus 2}\)