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

• Label: 665.2.j
• Level: $665$
• Weight: $2$
• Character orbit: 665.j
• Rep. character: $\chi_{665}(191,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $11$
• Sturm bound: $160$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 665 = 5 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	665.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(160\)
Trace bound:			\(7\)
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	96	72
Cusp forms	152	96	56
Eisenstein series	16	0	16

Trace form

96 * q + 4 * q^2 - 44 * q^4 + 4 * q^5 + 8 * q^6 - 24 * q^8 - 48 * q^9 + 12 * q^11 - 20 * q^12 - 4 * q^14 - 8 * q^15 - 28 * q^16 + 16 * q^17 - 16 * q^18 - 8 * q^20 - 4 * q^21 - 4 * q^23 + 4 * q^24 - 48 * q^25 + 24 * q^27 + 24 * q^28 - 8 * q^29 - 4 * q^30 - 4 * q^31 + 8 * q^32 + 8 * q^33 - 80 * q^34 + 4 * q^35 + 48 * q^36 + 16 * q^37 + 12 * q^38 + 8 * q^39 + 16 * q^41 + 72 * q^42 - 48 * q^43 + 32 * q^44 + 28 * q^46 + 20 * q^47 + 80 * q^48 + 8 * q^49 - 8 * q^50 - 24 * q^51 - 24 * q^52 - 8 * q^53 - 64 * q^54 - 16 * q^55 - 40 * q^56 + 40 * q^58 - 4 * q^59 - 12 * q^60 + 4 * q^61 - 64 * q^62 - 60 * q^63 + 56 * q^64 + 4 * q^65 + 56 * q^66 + 48 * q^67 + 28 * q^68 + 72 * q^69 - 4 * q^70 + 80 * q^71 - 28 * q^72 + 4 * q^73 - 48 * q^74 - 84 * q^77 + 16 * q^78 + 44 * q^79 + 12 * q^80 - 56 * q^81 - 48 * q^82 - 32 * q^83 + 88 * q^84 - 16 * q^85 + 68 * q^86 - 8 * q^87 + 32 * q^88 - 52 * q^89 + 28 * q^91 + 8 * q^92 - 28 * q^93 + 60 * q^94 - 24 * q^96 + 68 * 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.j.a	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.j.a	$2$	$0$	\(-2\)	\(-2\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
665.2.j.b	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.j.b	$2$	$0$	\(0\)	\(0\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
665.2.j.c	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.j.c	$2$	$0$	\(0\)	\(2\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
665.2.j.d	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.j.d	$2$	$0$	\(1\)	\(1\)	\(-1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
665.2.j.e	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.j.e	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
665.2.j.f	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	\(\Q(\sqrt{-3}) \)	None		✓			665.2.j.f	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
665.2.j.g	$665$	$2$	665.j	7.c	$3$	$6$	$3$	$5.310$	6.0.1415907.1	None		✓			665.2.j.g	$2$	$0$	\(-1\)	\(-1\)	\(-3\)	\(3\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{4}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
665.2.j.h	$665$	$2$	665.j	7.c	$3$	$16$	$8$	$5.310$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			665.2.j.h	$2$	$0$	\(-1\)	\(-2\)	\(-8\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}+\beta _{10})q^{2}+(-\beta _{6}+\beta _{8}+\beta _{9}+\cdots)q^{3}+\cdots\)
665.2.j.i	$665$	$2$	665.j	7.c	$3$	$16$	$8$	$5.310$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			665.2.j.i	$2$	$0$	\(-1\)	\(4\)	\(-8\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(\beta _{1}-\beta _{2}-\beta _{5}-\beta _{11}+\cdots)q^{3}+\cdots\)
665.2.j.j	$665$	$2$	665.j	7.c	$3$	$22$	$11$	$5.310$		None		✓			665.2.j.j	$2$	$0$	\(0\)	\(5\)	\(11\)	\(-11\)		$\mathrm{SU}(2)[C_{3}]$
665.2.j.k	$665$	$2$	665.j	7.c	$3$	$24$	$12$	$5.310$		None		✓	✓		665.2.j.k	$2$	$0$	\(4\)	\(-7\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(665, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)