Space of modular forms of level 2646, weight 2, and Character 2646.d

• Label: 2646.2.d
• Level: $2646$
• Weight: $2$
• Character orbit: 2646.d
• Rep. character: $\chi_{2646}(2645,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $6$
• Sturm bound: $1008$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1008\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2646, [\chi])\).

	Total	New	Old
Modular forms	552	52	500
Cusp forms	456	52	404
Eisenstein series	96	0	96

Trace form

\( 52 q - 52 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2646, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2646.2.d.a	$2646$	$2$	2646.d	21.c	$2$	$4$	$4$	$21.128$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}-q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}q^{8}+\cdots\)
2646.2.d.b	$2646$	$2$	2646.d	21.c	$2$	$4$	$4$	$21.128$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{2}-q^{4}-2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{8}+\cdots\)
2646.2.d.c	$2646$	$2$	2646.d	21.c	$2$	$4$	$4$	$21.128$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{2}-q^{4}+\zeta_{12}q^{8}+3\zeta_{12}q^{11}+\cdots\)
2646.2.d.d	$2646$	$2$	2646.d	21.c	$2$	$8$	$8$	$21.128$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}q^{2}-q^{4}+\zeta_{24}^{4}q^{5}-\zeta_{24}q^{8}+\cdots\)
2646.2.d.e	$2646$	$2$	2646.d	21.c	$2$	$16$	$16$	$21.128$	\(\Q(\zeta_{48})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{48}q^{2}-q^{4}+(\zeta_{48}^{9}+\zeta_{48}^{12})q^{5}+\cdots\)
2646.2.d.f	$2646$	$2$	2646.d	21.c	$2$	$16$	$16$	$21.128$	\(\Q(\zeta_{48})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{48}q^{2}-q^{4}+(-\zeta_{48}^{5}-\zeta_{48}^{8}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2646, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)