Space of modular forms of level 1960, weight 2, and Character 1960.g

• Label: 1960.2.g
• Level: $1960$
• Weight: $2$
• Character orbit: 1960.g
• Rep. character: $\chi_{1960}(1569,\cdot)$
• Character field: $\Q$
• Dimension: $62$
• Newform subspaces: $7$
• Sturm bound: $672$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(672\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1960, [\chi])\).

	Total	New	Old
Modular forms	368	62	306
Cusp forms	304	62	242
Eisenstein series	64	0	64

Trace form

\( 62 q - 2 q^{5} - 66 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1960, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1960.2.g.a	$1960$	$2$	1960.g	5.b	$2$	$2$	$2$	$15.651$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-2-i)q^{5}+2q^{9}-q^{11}+\cdots\)
1960.2.g.b	$1960$	$2$	1960.g	5.b	$2$	$2$	$2$	$15.651$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(1-i)q^{5}-q^{9}-4q^{11}+2iq^{13}+\cdots\)
1960.2.g.c	$1960$	$2$	1960.g	5.b	$2$	$6$	$6$	$15.651$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.g.d	$1960$	$2$	1960.g	5.b	$2$	$8$	$8$	$15.651$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}-\beta _{6}q^{5}-\beta _{2}q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
1960.2.g.e	$1960$	$2$	1960.g	5.b	$2$	$12$	$12$	$15.651$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
1960.2.g.f	$1960$	$2$	1960.g	5.b	$2$	$12$	$12$	$15.651$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{5}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
1960.2.g.g	$1960$	$2$	1960.g	5.b	$2$	$20$	$20$	$15.651$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{25}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{17}q^{3}-\beta _{16}q^{5}+(-1+\beta _{1})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)