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

• Label: 4620.2.h
• Level: $4620$
• Weight: $2$
• Character orbit: 4620.h
• Rep. character: $\chi_{4620}(1849,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $7$
• Sturm bound: $2304$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 4620 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4620.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(2304\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(13\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	1176	64	1112
Cusp forms	1128	64	1064
Eisenstein series	48	0	48

Trace form

\( 64 q - 64 q^{9} + O(q^{10}) \)

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.h.a	$4620$	$2$	4620.h	5.b	$2$	$2$	$2$	$36.891$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(1-2i)q^{5}-iq^{7}-q^{9}-q^{11}+\cdots\)
4620.2.h.b	$4620$	$2$	4620.h	5.b	$2$	$2$	$2$	$36.891$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(2-i)q^{5}-iq^{7}-q^{9}-q^{11}+\cdots\)
4620.2.h.c	$4620$	$2$	4620.h	5.b	$2$	$2$	$2$	$36.891$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(2+i)q^{5}+iq^{7}-q^{9}+q^{11}+\cdots\)
4620.2.h.d	$4620$	$2$	4620.h	5.b	$2$	$14$	$14$	$36.891$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{4}q^{5}+\beta _{3}q^{7}-q^{9}-q^{11}+\cdots\)
4620.2.h.e	$4620$	$2$	4620.h	5.b	$2$	$14$	$14$	$36.891$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-q^{9}+q^{11}+\cdots\)
4620.2.h.f	$4620$	$2$	4620.h	5.b	$2$	$14$	$14$	$36.891$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+\beta _{7}q^{5}+\beta _{6}q^{7}-q^{9}-q^{11}+\cdots\)
4620.2.h.g	$4620$	$2$	4620.h	5.b	$2$	$16$	$16$	$36.891$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{3}+\beta _{4}q^{5}+\beta _{8}q^{7}-q^{9}+q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4620, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2310, [\chi])\)\(^{\oplus 2}\)