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

• Label: 325.2.d
• Level: $325$
• Weight: $2$
• Character orbit: 325.d
• Rep. character: $\chi_{325}(324,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $6$
• Sturm bound: $70$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(70\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	40	24	16
Cusp forms	28	20	8
Eisenstein series	12	4	8

Trace form

\( 20 q + 24 q^{4} - 8 q^{9} + O(q^{10}) \)

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.d.a	$325$	$2$	325.d	65.d	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{2}+iq^{3}+2q^{4}-2iq^{6}-2q^{7}+\cdots\)
325.2.d.b	$325$	$2$	325.d	65.d	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+2iq^{3}-q^{4}-2iq^{6}+5q^{7}+\cdots\)
325.2.d.c	$325$	$2$	325.d	65.d	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+2iq^{3}-q^{4}+2iq^{6}-5q^{7}+\cdots\)
325.2.d.d	$325$	$2$	325.d	65.d	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{2}+iq^{3}+2q^{4}+2iq^{6}+2q^{7}+\cdots\)
325.2.d.e	$325$	$2$	325.d	65.d	$2$	$6$	$6$	$2.595$	6.0.5089536.1	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
325.2.d.f	$325$	$2$	325.d	65.d	$2$	$6$	$6$	$2.595$	6.0.5089536.1	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)

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

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