Space of modular forms of level 3087, weight 2, and Character 3087.c

• Label: 3087.2.c
• Level: $3087$
• Weight: $2$
• Character orbit: 3087.c
• Rep. character: $\chi_{3087}(3086,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $784$
• Trace bound: $16$

Defining parameters

Level:	\( N \)	\(=\)	\( 3087 = 3^{2} \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3087.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(784\)
Trace bound:			\(16\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3087, [\chi])\).

	Total	New	Old
Modular forms	420	96	324
Cusp forms	364	96	268
Eisenstein series	56	0	56

Trace form

\( 96 q - 96 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3087, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3087.2.c.a	$3087$	$2$	3087.c	21.c	$2$	$12$	$12$	$24.650$	12.0.\(\cdots\).1	\(\Q(\sqrt{-7}) \)		✓			3087.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{7}+\beta _{9}+\beta _{11})q^{2}+(-2-\beta _{6}+\cdots)q^{4}+\cdots\)
3087.2.c.b	$3087$	$2$	3087.c	21.c	$2$	$12$	$12$	$24.650$	12.0.\(\cdots\).1	\(\Q(\sqrt{-7}) \)		✓			3087.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{3}+\beta _{7}-\beta _{9}-\beta _{11})q^{2}+(-2+\cdots)q^{4}+\cdots\)
3087.2.c.c	$3087$	$2$	3087.c	21.c	$2$	$24$	$24$	$24.650$		None		✓			3087.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
3087.2.c.d	$3087$	$2$	3087.c	21.c	$2$	$48$	$48$	$24.650$		None		✓	✓		3087.2.c.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3087, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3087, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1029, [\chi])\)\(^{\oplus 2}\)