Space of modular forms of level 3120, weight 1, and Character 3120.be

• Label: 3120.1.be
• Level: $3120$
• Weight: $1$
• Character orbit: 3120.be
• Rep. character: $\chi_{3120}(1169,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $5$
• Sturm bound: $672$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3120.be (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 195 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(672\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3120, [\chi])\).

	Total	New	Old
Modular forms	64	12	52
Cusp forms	40	8	32
Eisenstein series	24	4	20

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

\( 8 q + 4 q^{25} - 4 q^{39} - 4 q^{49} + 4 q^{51} + 8 q^{55} - 4 q^{61} - 4 q^{69} + 4 q^{75} + 4 q^{79} + 8 q^{81} + 4 q^{91}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3120, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3120.1.be.a	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-195}) \)	None	✓				780.1.o.a	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)	$1$		\(q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
3120.1.be.b	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-195}) \)	None	✓				780.1.o.a	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)	$1$		\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3120.1.be.c	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-195}) \)	None	✓				780.1.o.a	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)	$1$		\(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
3120.1.be.d	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-195}) \)	None	✓				780.1.o.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)	$1$		\(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
3120.1.be.e	$3120$	$1$	3120.be	195.e	$2$	$4$	$4$	$1.557$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-39}) \)	None			✓		195.1.e.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}^{2}q^{3}+\zeta_{8}^{3}q^{5}-q^{9}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3120, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3120, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 3}\)