Space of modular forms of level 4620, weight 2, and Character 4620.f

• Label: 4620.2.f
• Level: $4620$
• Weight: $2$
• Character orbit: 4620.f
• Rep. character: $\chi_{4620}(769,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $2304$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 4620 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4620.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 385 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(2304\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(13\), \(19\), \(43\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4620, [\chi])\).

	Total	New	Old
Modular forms	1176	96	1080
Cusp forms	1128	96	1032
Eisenstein series	48	0	48

Trace form

\( 96 q + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4620, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4620.2.f.a	$4620$	$2$	4620.f	385.h	$2$	$4$	$4$	$36.891$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$1$	\(0\)	\(-4\)	\(-3\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
4620.2.f.b	$4620$	$2$	4620.f	385.h	$2$	$4$	$4$	$36.891$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-4\)	\(-3\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+(2+\beta _{2}+\cdots)q^{7}+\cdots\)
4620.2.f.c	$4620$	$2$	4620.f	385.h	$2$	$4$	$4$	$36.891$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(4\)	\(3\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
4620.2.f.d	$4620$	$2$	4620.f	385.h	$2$	$4$	$4$	$36.891$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(4\)	\(3\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+(2+\beta _{2})q^{7}+\cdots\)
4620.2.f.e	$4620$	$2$	4620.f	385.h	$2$	$40$	$40$	$36.891$		None		$4$	$0$	\(0\)	\(-40\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
4620.2.f.f	$4620$	$2$	4620.f	385.h	$2$	$40$	$40$	$36.891$		None		$4$	$0$	\(0\)	\(40\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(4620, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4620, [\chi]) \cong \)