Space of modular forms of level 612, weight 1, and Character 612.e

• Label: 612.1.e
• Level: $612$
• Weight: $1$
• Character orbit: 612.e
• Rep. character: $\chi_{612}(271,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 612 = 2^{2} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	612.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 68 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(612, [\chi])\).

	Total	New	Old
Modular forms	12	3	9
Cusp forms	4	1	3
Eisenstein series	8	2	6

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

\( q + q^{2} + q^{4} + q^{8} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(612, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
612.1.e.a	$612$	$1$	612.e	68.d	$2$	$1$	$1$	$0.305$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \)	\(\Q(\sqrt{17}) \)	✓		✓	✓	68.1.d.a	$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}-2q^{13}+q^{16}-q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(612, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(612, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 2}\)