Space of modular forms of level 325, weight 2, and Character 325.r

• Label: 325.2.r
• Level: $325$
• Weight: $2$
• Character orbit: 325.r
• Rep. character: $\chi_{325}(14,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $120$
• Newform subspaces: $1$
• Sturm bound: $70$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.r (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(70\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(325, [\chi])\).

	Total	New	Old
Modular forms	152	120	32
Cusp forms	136	120	16
Eisenstein series	16	0	16

Trace form

\( 120 q + 30 q^{4} - 10 q^{5} + 4 q^{6} - 30 q^{8} + 26 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(325, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
325.2.r.a	$325$	$2$	325.r	25.e	$10$	$120$	$30$	$2.595$		None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(325, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(325, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)