Space of modular forms of level 665, weight 2, and Character 665.l

• Label: 665.2.l
• Level: $665$
• Weight: $2$
• Character orbit: 665.l
• Rep. character: $\chi_{665}(11,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $104$
• Newform subspaces: $7$
• Sturm bound: $160$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 665 = 5 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	665.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(160\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(665, [\chi])\).

	Total	New	Old
Modular forms	168	104	64
Cusp forms	152	104	48
Eisenstein series	16	0	16

Trace form

\( 104 q - 4 q^{3} + 96 q^{4} - 2 q^{7} - 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(665, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
665.2.l.a	$665$	$2$	665.l	133.h	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.k.c	$2$	$0$	\(-2\)	\(1\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+\zeta_{6}q^{3}-q^{4}-q^{5}-\zeta_{6}q^{6}+\cdots\)
665.2.l.b	$665$	$2$	665.l	133.h	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.k.d	$2$	$0$	\(-2\)	\(1\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+\zeta_{6}q^{3}-q^{4}-q^{5}-\zeta_{6}q^{6}+\cdots\)
665.2.l.c	$665$	$2$	665.l	133.h	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.k.b	$2$	$0$	\(2\)	\(1\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+\zeta_{6}q^{3}-q^{4}+q^{5}+\zeta_{6}q^{6}+\cdots\)
665.2.l.d	$665$	$2$	665.l	133.h	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.k.a	$2$	$0$	\(2\)	\(3\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+3\zeta_{6}q^{3}-q^{4}+q^{5}+3\zeta_{6}q^{6}+\cdots\)
665.2.l.e	$665$	$2$	665.l	133.h	$3$	$4$	$2$	$5.310$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		✓			665.2.k.e	$2$	$0$	\(0\)	\(2\)	\(4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}-\beta _{2}q^{3}+5q^{4}+q^{5}+(\beta _{1}+\cdots)q^{6}+\cdots\)
665.2.l.f	$665$	$2$	665.l	133.h	$3$	$44$	$22$	$5.310$		None		✓			665.2.k.f	$2$	$0$	\(0\)	\(-8\)	\(44\)	\(5\)		$\mathrm{SU}(2)[C_{3}]$
665.2.l.g	$665$	$2$	665.l	133.h	$3$	$48$	$24$	$5.310$		None		✓	✓		665.2.k.g	$2$	$0$	\(0\)	\(-4\)	\(-48\)	\(9\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(665, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(665, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)