Space of modular forms of level 624, weight 2, and Character 624.u

• Label: 624.2.u
• Level: $624$
• Weight: $2$
• Character orbit: 624.u
• Rep. character: $\chi_{624}(5,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $216$
• Newform subspaces: $3$
• Sturm bound: $224$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.u (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 624 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(224\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(624, [\chi])\).

	Total	New	Old
Modular forms	232	232	0
Cusp forms	216	216	0
Eisenstein series	16	16	0

Trace form

\( 216 q - 4 q^{3} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(624, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
624.2.u.a	$624$	$2$	624.u	624.u	$4$	$4$	$2$	$4.983$	\(\Q(i, \sqrt{11})\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{2})q^{2}-\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots\)
624.2.u.b	$624$	$2$	624.u	624.u	$4$	$4$	$2$	$4.983$	\(\Q(i, \sqrt{11})\)	None		$2$	$0$	\(4\)	\(-2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{2})q^{2}+\beta _{3}q^{3}-2\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots\)
624.2.u.c	$624$	$2$	624.u	624.u	$4$	$208$	$104$	$4.983$		None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{4}]$