Space of modular forms of level 1764, weight 4, and Character 1764.t

• Label: 1764.4.t
• Level: $1764$
• Weight: $4$
• Character orbit: 1764.t
• Rep. character: $\chi_{1764}(521,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $1344$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(1344\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1764, [\chi])\).

	Total	New	Old
Modular forms	2112	80	2032
Cusp forms	1920	80	1840
Eisenstein series	192	0	192

Trace form

\( 80 q + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1764, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1764.4.t.a	$1764$	$4$	1764.t	21.g	$6$	$16$	$8$	$104.079$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{11}q^{5}+(-\beta _{2}-\beta _{4})q^{11}+(\beta _{12}+\cdots)q^{13}+\cdots\)
1764.4.t.b	$1764$	$4$	1764.t	21.g	$6$	$16$	$8$	$104.079$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{9}q^{5}+(\beta _{3}+\beta _{5})q^{11}+(-1-\beta _{1}+\cdots)q^{13}+\cdots\)
1764.4.t.c	$1764$	$4$	1764.t	21.g	$6$	$48$	$24$	$104.079$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

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