Space of modular forms of level 3100, weight 1, and Character 3100.t

• Label: 3100.1.t
• Level: $3100$
• Weight: $1$
• Character orbit: 3100.t
• Rep. character: $\chi_{3100}(1699,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3100.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 620 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3100, [\chi])\).

	Total	New	Old
Modular forms	32	16	16
Cusp forms	8	8	0
Eisenstein series	24	8	16

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

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

Trace form

\( 8 q + 8 q^{4} - 4 q^{6} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3100, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3100.1.t.a	$3100$	$1$	3100.t	620.o	$6$	$4$	$2$	$1.547$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(-4\)	\(2\)	\(0\)	\(2\)	$1$		\(q-q^{2}+\zeta_{12}^{2}q^{3}+q^{4}-\zeta_{12}^{2}q^{6}+\cdots\)
3100.1.t.b	$3100$	$1$	3100.t	620.o	$6$	$4$	$2$	$1.547$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(4\)	\(-2\)	\(0\)	\(-2\)	$1$		\(q+q^{2}-\zeta_{12}^{2}q^{3}+q^{4}-\zeta_{12}^{2}q^{6}+\cdots\)