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 + 8 * q^10 - 2 * q^11 - 8 * q^12 - 16 * q^13 - 12 * q^14 + 80 * q^16 - 4 * q^17 - 6 * q^19 + 6 * q^21 - 4 * q^22 + 104 * q^25 - 6 * q^26 + 32 * q^27 - 32 * q^28 - 4 * q^29 - 10 * q^31 + 20 * q^32 + 32 * q^33 - 8 * q^34 - 4 * q^35 - 52 * q^36 + 16 * q^37 - 56 * q^38 + 18 * q^39 + 24 * q^40 - 6 * q^41 - 22 * q^42 - 2 * q^43 - 28 * q^44 + 18 * q^46 + 12 * q^47 - 118 * q^48 - 26 * q^49 - 16 * q^51 - 44 * q^52 + 8 * q^53 - 112 * q^54 - 34 * q^56 - 22 * q^57 - 22 * q^58 - 18 * q^59 - 8 * q^61 + 38 * q^62 + 18 * q^63 + 72 * q^64 + 12 * q^65 - 8 * q^66 + 4 * q^67 - 78 * q^68 - 24 * q^69 - 24 * q^70 + 72 * q^72 + 2 * q^73 + 42 * q^74 - 4 * q^75 + 38 * q^76 + 50 * q^77 - 76 * q^78 - 40 * q^79 - 28 * q^81 - 42 * q^82 + 12 * q^83 - 92 * q^84 - 28 * q^86 - 34 * q^87 - 12 * q^88 + 32 * q^89 - 38 * q^90 - 46 * q^91 + 68 * q^92 + 44 * q^93 + 4 * q^94 - 12 * q^95 + 104 * q^96 - 66 * q^97 + 160 * q^98 - 92 * q^99

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

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