Space of modular forms of level 624, weight 1, and Character 624.l

• Label: 624.1.l
• Level: $624$
• Weight: $1$
• Character orbit: 624.l
• Rep. character: $\chi_{624}(545,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	624.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(624, [\chi])\).

	Total	New	Old
Modular forms	18	3	15
Cusp forms	6	1	5
Eisenstein series	12	2	10

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

\( q + q^{3} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
624.1.l.a	$624$	$1$	624.l	39.d	$2$	$1$	$1$	$0.311$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \)	\(\Q(\sqrt{13}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}+q^{9}-q^{13}-q^{25}+q^{27}-q^{39}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(624, [\chi]) \cong \)