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

• Label: 1764.2.bm
• Level: $1764$
• Weight: $2$
• Character orbit: 1764.bm
• Rep. character: $\chi_{1764}(1685,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $672$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.bm (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(672\)
Trace bound:			\(9\)
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 - 2 * q^9 - 3 * q^13 + 9 * q^15 + 9 * q^17 + 80 * q^25 + 9 * q^27 - 6 * q^29 - 6 * q^31 + 27 * q^33 - q^37 - q^39 - 6 * q^41 + 2 * q^43 + 15 * q^45 + 18 * q^47 - 27 * q^51 + 12 * q^53 - 11 * q^57 + 15 * q^59 - 3 * q^61 + 57 * q^65 + 7 * q^67 + 21 * q^69 + 15 * q^75 - 5 * q^79 - 18 * q^81 - 12 * q^85 + 3 * q^87 + 21 * q^89 + 105 * q^93 - 30 * q^95 - 3 * q^97 + 41 * 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.bm.a	$1764$	$2$	1764.bm	63.s	$6$	$16$	$8$	$14.086$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					252.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{12})q^{3}+(\beta _{7}-\beta _{9})q^{5}+(-\beta _{5}+\cdots)q^{9}+\cdots\)
1764.2.bm.b	$1764$	$2$	1764.bm	63.s	$6$	$16$	$8$	$14.086$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					252.2.x.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}+\beta _{15}q^{5}+\beta _{2}q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1764.2.bm.c	$1764$	$2$	1764.bm	63.s	$6$	$48$	$24$	$14.086$		None		✓	✓		1764.2.x.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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