Space of modular forms of level 1764, weight 2, and Character 1764.l

• Label: 1764.2.l
• Level: $1764$
• Weight: $2$
• Character orbit: 1764.l
• Rep. character: $\chi_{1764}(949,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $10$
• Sturm bound: $672$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(672\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1764, [\chi])\).

	Total	New	Old
Modular forms	720	80	640
Cusp forms	624	80	544
Eisenstein series	96	0	96

Trace form

80 * q - 8 * q^5 - 6 * q^9 - 8 * q^11 + q^13 - 17 * q^15 + 5 * q^17 - 2 * q^19 + 22 * q^23 + 80 * q^25 - 9 * q^27 - 6 * q^29 - 2 * q^31 - 5 * q^33 + q^37 + 41 * q^39 + 24 * q^41 - 2 * q^43 + 7 * q^45 + 6 * q^47 + 5 * q^51 + 22 * q^53 + 12 * q^55 + 15 * q^57 + 7 * q^59 + 13 * q^61 - 11 * q^65 + 7 * q^67 + 43 * q^69 + 38 * q^71 - 14 * q^73 - q^75 + 7 * q^79 - 58 * q^81 + 26 * q^83 + 12 * q^85 + 5 * q^87 + 21 * q^89 - 11 * q^93 + 54 * q^95 + q^97 - 23 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1764, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1764.2.l.a	$1764$	$2$	1764.l	63.g	$3$	$2$	$1$	$14.086$	\(\Q(\sqrt{-3}) \)	None					36.2.e.a	$2$	$1$	\(0\)	\(-3\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\zeta_{6})q^{3}-3q^{5}+3\zeta_{6}q^{9}+3q^{11}+\cdots\)
1764.2.l.b	$1764$	$2$	1764.l	63.g	$3$	$2$	$1$	$14.086$	\(\Q(\sqrt{-3}) \)	None					252.2.i.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-2\zeta_{6})q^{3}-2q^{5}-3q^{9}+4q^{11}+\cdots\)
1764.2.l.c	$1764$	$2$	1764.l	63.g	$3$	$2$	$1$	$14.086$	\(\Q(\sqrt{-3}) \)	None					36.2.e.a	$2$	$0$	\(0\)	\(3\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\zeta_{6})q^{3}+3q^{5}+3\zeta_{6}q^{9}+3q^{11}+\cdots\)
1764.2.l.d	$1764$	$2$	1764.l	63.g	$3$	$6$	$3$	$14.086$	6.0.309123.1	None					252.2.j.b	$2$	$0$	\(0\)	\(-4\)	\(-6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{4})q^{3}+(-1-\beta _{2}-\beta _{4}-\beta _{5})q^{5}+\cdots\)
1764.2.l.e	$1764$	$2$	1764.l	63.g	$3$	$6$	$3$	$14.086$	6.0.309123.1	None					252.2.j.a	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
1764.2.l.f	$1764$	$2$	1764.l	63.g	$3$	$6$	$3$	$14.086$	6.0.309123.1	None					252.2.j.a	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+(\beta _{2}+\beta _{3})q^{5}+\cdots\)
1764.2.l.g	$1764$	$2$	1764.l	63.g	$3$	$6$	$3$	$14.086$	6.0.309123.1	None					252.2.j.b	$2$	$0$	\(0\)	\(4\)	\(6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4})q^{3}+(1+\beta _{2}+\beta _{4}+\beta _{5})q^{5}+\cdots\)
1764.2.l.h	$1764$	$2$	1764.l	63.g	$3$	$12$	$6$	$14.086$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1764.2.j.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}+\beta _{9})q^{3}+\beta _{11}q^{5}+(1-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots\)
1764.2.l.i	$1764$	$2$	1764.l	63.g	$3$	$14$	$7$	$14.086$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					252.2.i.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{4})q^{3}+(\beta _{5}-\beta _{10})q^{5}+(1+\cdots)q^{9}+\cdots\)
1764.2.l.j	$1764$	$2$	1764.l	63.g	$3$	$24$	$12$	$14.086$		None		✓	✓		1764.2.j.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1764, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)