Space of modular forms of level 2912, weight 2, and Character 2912.i

• Label: 2912.2.i
• Level: $2912$
• Weight: $2$
• Character orbit: 2912.i
• Rep. character: $\chi_{2912}(337,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $1$
• Sturm bound: $896$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2912 = 2^{5} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2912.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(896\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2912, [\chi])\).

	Total	New	Old
Modular forms	464	84	380
Cusp forms	432	84	348
Eisenstein series	32	0	32

Trace form

\( 84 q - 84 q^{9} + 8 q^{17} + 24 q^{23} + 92 q^{25} + 24 q^{39} - 84 q^{49} - 32 q^{55} - 24 q^{65} + 40 q^{79} + 84 q^{81} + 48 q^{87} + 16 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2912, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2912.2.i.a	$2912$	$2$	2912.i	104.e	$2$	$84$	$84$	$23.252$		None			✓	✓	728.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2912, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 3}\)