Space of modular forms of level 40, weight 4, and Character 40.c

• Label: 40.4.c
• Level: $40$
• Weight: $4$
• Character orbit: 40.c
• Rep. character: $\chi_{40}(9,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	40.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(40, [\chi])\).

	Total	New	Old
Modular forms	22	4	18
Cusp forms	14	4	10
Eisenstein series	8	0	8

Trace form

4 * q - 4 * q^5 - 4 * q^9 + 80 * q^11 - 80 * q^15 - 80 * q^19 - 272 * q^21 + 276 * q^25 + 280 * q^29 + 384 * q^31 - 304 * q^35 - 224 * q^39 - 1048 * q^41 + 772 * q^45 + 492 * q^49 + 1920 * q^51 - 1616 * q^55 - 1392 * q^59 - 1384 * q^61 + 608 * q^65 + 112 * q^69 + 1376 * q^71 + 160 * q^75 + 1472 * q^79 - 1484 * q^81 + 1152 * q^85 + 1320 * q^89 + 992 * q^91 - 1456 * q^95 - 3152 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(40, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
40.4.c.a	$40$	$4$	40.c	5.b	$2$	$4$	$4$	$2.360$	\(\Q(i, \sqrt{6})\)	None		✓	✓	✓	40.4.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(40, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(40, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)