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

• Label: 665.2.i
• Level: $665$
• Weight: $2$
• Character orbit: 665.i
• Rep. character: $\chi_{665}(106,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $8$
• Sturm bound: $160$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 665 = 5 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	665.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(160\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	168	80	88
Cusp forms	152	80	72
Eisenstein series	16	0	16

Trace form

80 * q + 4 * q^2 - 4 * q^3 - 44 * q^4 - 8 * q^6 - 24 * q^8 - 52 * q^9 - 4 * q^10 + 8 * q^11 + 24 * q^12 + 8 * q^15 - 52 * q^16 + 20 * q^17 - 16 * q^18 + 24 * q^19 - 4 * q^22 + 12 * q^23 + 4 * q^24 - 40 * q^25 - 16 * q^26 + 32 * q^27 - 4 * q^29 - 32 * q^30 - 16 * q^31 + 68 * q^32 + 32 * q^33 - 4 * q^34 - 68 * q^36 - 8 * q^37 + 4 * q^38 - 8 * q^39 + 24 * q^40 - 20 * q^41 + 24 * q^43 - 16 * q^44 + 16 * q^45 + 120 * q^46 - 24 * q^47 - 60 * q^48 + 80 * q^49 - 8 * q^50 - 8 * q^51 - 52 * q^52 + 32 * q^53 - 28 * q^54 + 48 * q^57 + 48 * q^58 - 16 * q^59 + 12 * q^60 + 48 * q^61 - 4 * q^62 - 8 * q^63 + 16 * q^64 - 32 * q^65 - 12 * q^66 + 4 * q^67 - 128 * q^68 - 16 * q^69 + 4 * q^70 - 24 * q^71 - 4 * q^72 - 20 * q^73 + 48 * q^74 + 8 * q^75 - 88 * q^76 + 8 * q^78 - 4 * q^79 - 120 * q^81 + 92 * q^82 - 64 * q^83 + 56 * q^84 - 16 * q^85 + 20 * q^86 + 16 * q^88 - 28 * q^89 - 32 * q^90 + 28 * q^92 + 48 * q^93 + 56 * q^94 + 12 * q^95 + 48 * q^96 - 60 * q^97 + 4 * q^98 + 48 * 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.i.a	$665$	$2$	665.i	19.c	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.i.a	$2$	$1$	\(-2\)	\(-2\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\cdots\)
665.2.i.b	$665$	$2$	665.i	19.c	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.i.b	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
665.2.i.c	$665$	$2$	665.i	19.c	$3$	$4$	$2$	$5.310$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		✓			665.2.i.c	$2$	$1$	\(-4\)	\(-2\)	\(-2\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-2\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
665.2.i.d	$665$	$2$	665.i	19.c	$3$	$6$	$3$	$5.310$	6.0.954288.1	None		✓			665.2.i.d	$2$	$0$	\(0\)	\(-2\)	\(3\)	\(6\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
665.2.i.e	$665$	$2$	665.i	19.c	$3$	$14$	$7$	$5.310$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			665.2.i.e	$2$	$0$	\(1\)	\(-3\)	\(7\)	\(14\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}+\beta _{6}+\beta _{8})q^{2}+\beta _{7}q^{3}+(-3+\cdots)q^{4}+\cdots\)
665.2.i.f	$665$	$2$	665.i	19.c	$3$	$16$	$8$	$5.310$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			665.2.i.f	$2$	$0$	\(1\)	\(5\)	\(-8\)	\(16\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(1+\beta _{7}+\beta _{8}-\beta _{12})q^{3}+\cdots\)
665.2.i.g	$665$	$2$	665.i	19.c	$3$	$16$	$8$	$5.310$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			665.2.i.g	$2$	$0$	\(3\)	\(1\)	\(-8\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+\beta _{15}q^{3}+(\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
665.2.i.h	$665$	$2$	665.i	19.c	$3$	$20$	$10$	$5.310$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		665.2.i.h	$2$	$0$	\(3\)	\(-1\)	\(10\)	\(-20\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{6}-\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(665, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)