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

• Label: 3104.1.y
• Level: $3104$
• Weight: $1$
• Character orbit: 3104.y
• Rep. character: $\chi_{3104}(255,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• 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.y (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 388 \)
Character field:			\(\Q(\zeta_{6})\)
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	36	4	32
Cusp forms	20	4	16
Eisenstein series	16	0	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	4	0	0

Trace form

4 * q + 2 * q^5 - 2 * q^13 + 2 * q^17 - 2 * q^21 - 2 * q^29 + 4 * q^33 - 2 * q^37 + 2 * q^41 + 2 * q^53 + 4 * q^57 + 2 * q^61 + 2 * q^65 + 4 * q^69 - 2 * q^73 - 4 * q^77 + 2 * q^81 + 4 * q^85 - 8 * q^89 - 2 * q^93 - 4 * q^97

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.y.a	$3104$	$1$	3104.y	388.i	$6$	$4$	$2$	$1.549$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		✓	✓	✓	3104.1.y.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{5}+\zeta_{12}q^{7}+\zeta_{12}^{5}q^{11}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3104, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(388, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1552, [\chi])\)\(^{\oplus 2}\)