Space of modular forms of level 1638, weight 2, and Character 1638.dt

• Label: 1638.2.dt
• Level: $1638$
• Weight: $2$
• Character orbit: 1638.dt
• Rep. character: $\chi_{1638}(1297,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $4$
• Sturm bound: $672$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.dt (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(672\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1638, [\chi])\).

	Total	New	Old
Modular forms	704	92	612
Cusp forms	640	92	548
Eisenstein series	64	0	64

Trace form

\( 92 q - 92 q^{4} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1638, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1638.2.dt.a	$1638$	$2$	1638.dt	91.k	$6$	$16$	$8$	$13.079$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{12}+\beta _{13})q^{2}-q^{4}+(1+\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
1638.2.dt.b	$1638$	$2$	1638.dt	91.k	$6$	$20$	$10$	$13.079$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{10}-\beta _{11})q^{2}-q^{4}+\beta _{4}q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots\)
1638.2.dt.c	$1638$	$2$	1638.dt	91.k	$6$	$20$	$10$	$13.079$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{5}-\beta _{6})q^{2}-q^{4}+(-\beta _{8}+\beta _{16}+\cdots)q^{5}+\cdots\)
1638.2.dt.d	$1638$	$2$	1638.dt	91.k	$6$	$36$	$18$	$13.079$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1638, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)