Space of modular forms of level 312, weight 2, and Character 312.y

• Label: 312.2.y
• Level: $312$
• Weight: $2$
• Character orbit: 312.y
• Rep. character: $\chi_{312}(5,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $104$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.y (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 312 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(312, [\chi])\).

	Total	New	Old
Modular forms	120	120	0
Cusp forms	104	104	0
Eisenstein series	16	16	0

Trace form

\( 104 q - 12 q^{6} - 8 q^{7} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(312, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
312.2.y.a	$312$	$2$	312.y	312.y	$4$	$104$	$52$	$2.491$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{4}]$