Space of modular forms of level 40, weight 8, and Character 40.c

• Label: 40.8.c
• Level: $40$
• Weight: $8$
• Character orbit: 40.c
• Rep. character: $\chi_{40}(9,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	40.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(40, [\chi])\).

	Total	New	Old
Modular forms	46	10	36
Cusp forms	38	10	28
Eisenstein series	8	0	8

Trace form

\( 10 q - 194 q^{5} - 6586 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(40, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
40.8.c.a	$40$	$8$	40.c	5.b	$2$	$2$	$2$	$12.495$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(550\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+17iq^{3}+(275+5^{2}i)q^{5}-53iq^{7}+\cdots\)
40.8.c.b	$40$	$8$	40.c	5.b	$2$	$8$	$8$	$12.495$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-744\)	\(0\)	$2^{38}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-93-\beta _{1}+\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(40, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(40, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)