Space of modular forms of level 496, weight 1, and Character 496.e

• Label: 496.1.e
• Level: $496$
• Weight: $1$
• Character orbit: 496.e
• Rep. character: $\chi_{496}(433,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 496 = 2^{4} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	496.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(496, [\chi])\).

	Total	New	Old
Modular forms	12	2	10
Cusp forms	6	1	5
Eisenstein series	6	1	5

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

\( q - q^{5} + q^{7} + q^{9} + q^{19} - q^{31} - q^{35} - q^{41} - q^{45} - 2 q^{47} + q^{59} + q^{63} - 2 q^{67} + q^{71} + q^{81} - q^{95} - q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(496, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
496.1.e.a	$496$	$1$	496.e	31.b	$2$	$1$	$1$	$0.248$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-31}) \)	None	✓		✓	✓	31.1.b.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)	$1$		\(q-q^{5}+q^{7}+q^{9}+q^{19}-q^{31}-q^{35}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(496, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(496, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 5}\)