Space of modular forms of level 1665, weight 2, and Character 1665.c

• Label: 1665.2.c
• Level: $1665$
• Weight: $2$
• Character orbit: 1665.c
• Rep. character: $\chi_{1665}(334,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $7$
• Sturm bound: $456$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1665 = 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1665.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(456\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1665, [\chi])\).

	Total	New	Old
Modular forms	236	90	146
Cusp forms	220	90	130
Eisenstein series	16	0	16

Trace form

\( 90 q - 86 q^{4} + 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1665, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1665.2.c.a	$1665$	$2$	1665.c	5.b	$2$	$2$	$2$	$13.295$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2q^{4}+(1+2i)q^{5}+(-4+\cdots)q^{10}+\cdots\)
1665.2.c.b	$1665$	$2$	1665.c	5.b	$2$	$2$	$2$	$13.295$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}+(-1+2i)q^{5}+2iq^{7}-6q^{11}+\cdots\)
1665.2.c.c	$1665$	$2$	1665.c	5.b	$2$	$2$	$2$	$13.295$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}+(1+2i)q^{5}-2iq^{7}+6q^{11}+\cdots\)
1665.2.c.d	$1665$	$2$	1665.c	5.b	$2$	$8$	$8$	$13.295$	8.0.309760000.3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1665.2.c.e	$1665$	$2$	1665.c	5.b	$2$	$18$	$18$	$13.295$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{13})q^{2}+(-2+\beta _{3}+\beta _{4})q^{4}+\cdots\)
1665.2.c.f	$1665$	$2$	1665.c	5.b	$2$	$26$	$26$	$13.295$		None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1665.2.c.g	$1665$	$2$	1665.c	5.b	$2$	$32$	$32$	$13.295$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1665, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1665, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)