Space of modular forms of level 3104, weight 1, and Character 3104.dr

• Label: 3104.1.dr
• Level: $3104$
• Weight: $1$
• Character orbit: 3104.dr
• Rep. character: $\chi_{3104}(431,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $392$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3104 = 2^{5} \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3104.dr (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 776 \)
Character field:			\(\Q(\zeta_{24})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(392\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3104, [\chi])\).

	Total	New	Old
Modular forms	96	24	72
Cusp forms	32	8	24
Eisenstein series	64	16	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + 4 q^{3} - 12 q^{9} + 8 q^{19} - 12 q^{27} - 4 q^{51} + 4 q^{57} - 4 q^{59} + 8 q^{81} + 4 q^{89}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3104, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3104.1.dr.a	$3104$	$1$	3104.dr	776.ah	$24$	$8$	$1$	$1.549$	\(\Q(\zeta_{24})\)	$D_{24}$	\(\Q(\sqrt{-2}) \)	None			✓	✓	776.1.bh.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{24}^{4}+\zeta_{24}^{6})q^{3}+(-1+\zeta_{24}^{8}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3104, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3104, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(776, [\chi])\)\(^{\oplus 3}\)