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

• Label: 1764.2.t
• Level: $1764$
• Weight: $2$
• Character orbit: 1764.t
• Rep. character: $\chi_{1764}(521,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $3$
• Sturm bound: $672$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(672\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	768	28	740
Cusp forms	576	28	548
Eisenstein series	192	0	192

Trace form

\( 28 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1764.2.t.a	$1764$	$2$	1764.t	21.g	$6$	$4$	$2$	$14.086$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{11}+(1-2\beta _{1}+\cdots)q^{13}+\cdots\)
1764.2.t.b	$1764$	$2$	1764.t	21.g	$6$	$8$	$4$	$14.086$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{2}q^{5}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{11}+\cdots\)
1764.2.t.c	$1764$	$2$	1764.t	21.g	$6$	$16$	$8$	$14.086$	\(\Q(\zeta_{48})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{48}^{4}-\zeta_{48}^{15})q^{5}+(\zeta_{48}-\zeta_{48}^{5}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)