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

• Label: 624.2.d
• Level: $624$
• Weight: $2$
• Character orbit: 624.d
• Rep. character: $\chi_{624}(287,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $9$
• Sturm bound: $224$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(224\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	124	24	100
Cusp forms	100	24	76
Eisenstein series	24	0	24

Trace form

\( 24 q + 12 q^{9} + O(q^{10}) \)

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.d.a	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
624.2.d.b	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta )q^{3}-\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
624.2.d.c	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}+2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{9}+\cdots\)
624.2.d.d	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{9}+\cdots\)
624.2.d.e	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta )q^{3}+\beta q^{5}+\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
624.2.d.f	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
624.2.d.g	$624$	$2$	624.d	12.b	$2$	$4$	$4$	$4.983$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
624.2.d.h	$624$	$2$	624.d	12.b	$2$	$4$	$4$	$4.983$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+3q^{9}+2\beta _{2}q^{11}+\cdots\)
624.2.d.i	$624$	$2$	624.d	12.b	$2$	$4$	$4$	$4.983$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(624, [\chi]) \cong \)