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

• Label: 312.2.c
• Level: $312$
• Weight: $2$
• Character orbit: 312.c
• Rep. character: $\chi_{312}(25,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $112$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(112\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	64	6	58
Cusp forms	48	6	42
Eisenstein series	16	0	16

Trace form

\( 6 q + 2 q^{3} + 6 q^{9} + O(q^{10}) \)

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.c.a	$312$	$2$	312.c	13.b	$2$	$2$	$2$	$2.491$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+iq^{7}+q^{9}+iq^{11}+(3+i)q^{13}+\cdots\)
312.2.c.b	$312$	$2$	312.c	13.b	$2$	$2$	$2$	$2.491$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+iq^{5}+iq^{7}+q^{9}+2iq^{11}+\cdots\)
312.2.c.c	$312$	$2$	312.c	13.b	$2$	$2$	$2$	$2.491$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+2iq^{5}-iq^{7}+q^{9}+iq^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(312, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)