Space of modular forms of level 315, weight 4, and Character 315.d

• Label: 315.4.d
• Level: $315$
• Weight: $4$
• Character orbit: 315.d
• Rep. character: $\chi_{315}(64,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

	Total	New	Old
Modular forms	152	46	106
Cusp forms	136	46	90
Eisenstein series	16	0	16

Trace form

\( 46 q - 204 q^{4} + 22 q^{5} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
315.4.d.a	$315$	$4$	315.d	5.b	$2$	$6$	$6$	$18.586$	6.0.84052224.1	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1-2\beta _{2}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
315.4.d.b	$315$	$4$	315.d	5.b	$2$	$10$	$10$	$18.586$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(0\)	$2^{9}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+(-5+\beta _{1}+\beta _{5})q^{4}+(2+\beta _{1}+\cdots)q^{5}+\cdots\)
315.4.d.c	$315$	$4$	315.d	5.b	$2$	$10$	$10$	$18.586$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-4+\beta _{2})q^{4}+(-1+\beta _{7}+\cdots)q^{5}+\cdots\)
315.4.d.d	$315$	$4$	315.d	5.b	$2$	$20$	$20$	$18.586$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}\cdot 5^{2}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-5+\beta _{1})q^{4}+\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(315, [\chi]) \cong \)