Space of modular forms of level 1170, weight 2, and Character 1170.f

• Label: 1170.2.f
• Level: $1170$
• Weight: $2$
• Character orbit: 1170.f
• Rep. character: $\chi_{1170}(649,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $6$
• Sturm bound: $504$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(504\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\), \(83\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1170, [\chi])\).

	Total	New	Old
Modular forms	268	36	232
Cusp forms	236	36	200
Eisenstein series	32	0	32

Trace form

\( 36 q + 36 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1170, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1170.2.f.a	$1170$	$2$	1170.f	65.d	$2$	$4$	$4$	$9.342$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(-4\)	\(0\)	\(3\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.f.b	$1170$	$2$	1170.f	65.d	$2$	$4$	$4$	$9.342$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(4\)	\(0\)	\(-3\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1170.2.f.c	$1170$	$2$	1170.f	65.d	$2$	$6$	$6$	$9.342$	6.0.350464.1	None		$2$	$0$	\(-6\)	\(0\)	\(-2\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1170.2.f.d	$1170$	$2$	1170.f	65.d	$2$	$6$	$6$	$9.342$	6.0.350464.1	None		$2$	$0$	\(6\)	\(0\)	\(2\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.f.e	$1170$	$2$	1170.f	65.d	$2$	$8$	$8$	$9.342$	8.0.\(\cdots\).15	None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{5}q^{5}-\beta _{4}q^{7}-q^{8}+\cdots\)
1170.2.f.f	$1170$	$2$	1170.f	65.d	$2$	$8$	$8$	$9.342$	8.0.\(\cdots\).15	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{5}q^{5}-\beta _{4}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \)