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

• Label: 4620.2.be
• Level: $4620$
• Weight: $2$
• Character orbit: 4620.be
• Rep. character: $\chi_{4620}(3541,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $5$
• Sturm bound: $2304$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 4620 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4620.be (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(2304\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(13\)

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

\( 64 q - 64 q^{9} + 8 q^{11} - 64 q^{25} + 16 q^{37} - 32 q^{49} + 48 q^{53} - 16 q^{67} + 48 q^{71} + 32 q^{77} + 64 q^{81} + 48 q^{91} + 32 q^{93} - 8 q^{99}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4620.2.be.a	$4620$	$2$	4620.be	77.b	$2$	$4$	$4$	$36.891$	\(\Q(i, \sqrt{7})\)	None		✓			4620.2.be.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{1}q^{5}-\beta _{3}q^{7}-q^{9}+(2+\cdots)q^{11}+\cdots\)
4620.2.be.b	$4620$	$2$	4620.be	77.b	$2$	$4$	$4$	$36.891$	\(\Q(i, \sqrt{7})\)	None		✓			4620.2.be.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}-q^{9}+(2+\cdots)q^{11}+\cdots\)
4620.2.be.c	$4620$	$2$	4620.be	77.b	$2$	$12$	$12$	$36.891$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			4620.2.be.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}+\beta _{7}q^{5}+\beta _{8}q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)
4620.2.be.d	$4620$	$2$	4620.be	77.b	$2$	$12$	$12$	$36.891$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			4620.2.be.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{3}+\beta _{10}q^{5}+(-\beta _{3}+\beta _{4})q^{7}+\cdots\)
4620.2.be.e	$4620$	$2$	4620.be	77.b	$2$	$32$	$32$	$36.891$		None		✓	✓		4620.2.be.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(4620, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(770, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1155, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2310, [\chi])\)\(^{\oplus 2}\)