Space of modular forms of level 315, weight 2, and Character 315.d

• Label: 315.2.d
• Level: $315$
• Weight: $2$
• Character orbit: 315.d
• Rep. character: $\chi_{315}(64,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $5$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(11\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).

	Total	New	Old
Modular forms	56	14	42
Cusp forms	40	14	26
Eisenstein series	16	0	16

Trace form

\( 14 q - 8 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
315.2.d.a	$315$	$2$	315.d	5.b	$2$	$2$	$2$	$2.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2q^{4}+(2-i)q^{5}+iq^{7}+\cdots\)
315.2.d.b	$315$	$2$	315.d	5.b	$2$	$2$	$2$	$2.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(-2+i)q^{5}+iq^{7}+\cdots\)
315.2.d.c	$315$	$2$	315.d	5.b	$2$	$2$	$2$	$2.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(-1-2i)q^{5}-iq^{7}+\cdots\)
315.2.d.d	$315$	$2$	315.d	5.b	$2$	$2$	$2$	$2.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(2+i)q^{5}-iq^{7}+3iq^{8}+\cdots\)
315.2.d.e	$315$	$2$	315.d	5.b	$2$	$6$	$6$	$2.515$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{3}+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(315, [\chi]) \cong \)