Space of modular forms of level 2940, weight 2, and Character 2940.x

• Label: 2940.2.x
• Level: $2940$
• Weight: $2$
• Character orbit: 2940.x
• Rep. character: $\chi_{2940}(97,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $1344$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.x (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(1344\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2940, [\chi])\).

	Total	New	Old
Modular forms	1440	80	1360
Cusp forms	1248	80	1168
Eisenstein series	192	0	192

Trace form

\( 80 q - 16 q^{11} + 8 q^{15} - 24 q^{25} - 8 q^{37} - 56 q^{43} + 16 q^{51} - 32 q^{53} + 16 q^{57} + 40 q^{65} + 64 q^{67} + 48 q^{71} - 80 q^{81} + 88 q^{85} + 16 q^{93} - 56 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2940, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2940.2.x.a	$2940$	$2$	2940.x	35.f	$4$	$24$	$12$	$23.476$		None		✓			2940.2.x.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
2940.2.x.b	$2940$	$2$	2940.x	35.f	$4$	$24$	$12$	$23.476$		None		✓			2940.2.x.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
2940.2.x.c	$2940$	$2$	2940.x	35.f	$4$	$32$	$16$	$23.476$		None			✓		420.2.bo.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2940, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)