Space of modular forms of level 650, weight 2, and Character 650.c

• Label: 650.2.c
• Level: $650$
• Weight: $2$
• Character orbit: 650.c
• Rep. character: $\chi_{650}(649,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $6$
• Sturm bound: $210$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(210\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(650, [\chi])\).

	Total	New	Old
Modular forms	116	20	96
Cusp forms	92	20	72
Eisenstein series	24	0	24

Trace form

\( 20 q + 20 q^{4} - 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(650, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
650.2.c.a	$650$	$2$	650.c	65.d	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+iq^{3}+q^{4}-iq^{6}-3q^{7}-q^{8}+\cdots\)
650.2.c.b	$650$	$2$	650.c	65.d	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+iq^{3}+q^{4}-iq^{6}-q^{8}-q^{9}+\cdots\)
650.2.c.c	$650$	$2$	650.c	65.d	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+iq^{3}+q^{4}+iq^{6}+q^{8}-q^{9}+\cdots\)
650.2.c.d	$650$	$2$	650.c	65.d	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+iq^{3}+q^{4}+iq^{6}+3q^{7}+q^{8}+\cdots\)
650.2.c.e	$650$	$2$	650.c	65.d	$2$	$6$	$6$	$5.190$	6.0.126157824.1	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
650.2.c.f	$650$	$2$	650.c	65.d	$2$	$6$	$6$	$5.190$	6.0.126157824.1	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)