Space of modular forms of level 325, weight 4, and Character 325.d

• Label: 325.4.d
• Level: $325$
• Weight: $4$
• Character orbit: 325.d
• Rep. character: $\chi_{325}(324,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $5$
• Sturm bound: $140$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	325.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(140\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(325, [\chi])\).

	Total	New	Old
Modular forms	112	64	48
Cusp forms	100	60	40
Eisenstein series	12	4	8

Trace form

\( 60 q + 228 q^{4} - 528 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(325, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
325.4.d.a	$325$	$4$	325.d	65.d	$2$	$2$	$2$	$19.176$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(30\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{2}-iq^{3}+q^{4}+3iq^{6}+15q^{7}+\cdots\)
325.4.d.b	$325$	$4$	325.d	65.d	$2$	$2$	$2$	$19.176$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(-30\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{2}-iq^{3}+q^{4}-3iq^{6}-15q^{7}+\cdots\)
325.4.d.c	$325$	$4$	325.d	65.d	$2$	$14$	$14$	$19.176$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(108\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{6}q^{3}+(4-\beta _{2})q^{4}+(-\beta _{8}+\cdots)q^{6}+\cdots\)
325.4.d.d	$325$	$4$	325.d	65.d	$2$	$14$	$14$	$19.176$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(-108\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{6}q^{3}+(4-\beta _{2})q^{4}+(\beta _{8}+\cdots)q^{6}+\cdots\)
325.4.d.e	$325$	$4$	325.d	65.d	$2$	$28$	$28$	$19.176$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(325, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(325, [\chi]) \cong \)