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

• Label: 1170.2.o
• Level: $1170$
• Weight: $2$
• Character orbit: 1170.o
• Rep. character: $\chi_{1170}(53,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $504$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(504\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	536	48	488
Cusp forms	472	48	424
Eisenstein series	64	0	64

Trace form

\( 48 q - 16 q^{7} + O(q^{10}) \)

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.o.a	$1170$	$2$	1170.o	15.e	$4$	$12$	$6$	$9.342$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{2}+\beta _{9}q^{4}+(\beta _{1}+\beta _{3}+\beta _{4}+\beta _{11})q^{5}+\cdots\)
1170.2.o.b	$1170$	$2$	1170.o	15.e	$4$	$12$	$6$	$9.342$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{6}q^{4}+(-1-\beta _{3}+\beta _{7}+\cdots)q^{5}+\cdots\)
1170.2.o.c	$1170$	$2$	1170.o	15.e	$4$	$12$	$6$	$9.342$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}+\beta _{9}q^{4}+(-\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
1170.2.o.d	$1170$	$2$	1170.o	15.e	$4$	$12$	$6$	$9.342$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}-\beta _{6}q^{4}+(1+\beta _{3}-\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)