Space of modular forms of level 4680, weight 2, and Character 4680.l

• Label: 4680.2.l
• Level: $4680$
• Weight: $2$
• Character orbit: 4680.l
• Rep. character: $\chi_{4680}(2809,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $11$
• Sturm bound: $2016$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4680.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(2016\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4680, [\chi])\).

	Total	New	Old
Modular forms	1040	90	950
Cusp forms	976	90	886
Eisenstein series	64	0	64

Trace form

\( 90 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4680, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4680.2.l.a	$4680$	$2$	4680.l	5.b	$2$	$2$	$2$	$37.370$	\(\Q(\sqrt{-1}) \)	None					520.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+i)q^{5}+4iq^{7}+2q^{11}-iq^{13}+\cdots\)
4680.2.l.b	$4680$	$2$	4680.l	5.b	$2$	$2$	$2$	$37.370$	\(\Q(\sqrt{-1}) \)	None					1560.2.l.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-2i)q^{5}+iq^{7}-3q^{11}+iq^{13}+\cdots\)
4680.2.l.c	$4680$	$2$	4680.l	5.b	$2$	$2$	$2$	$37.370$	\(\Q(\sqrt{-1}) \)	None					1560.2.l.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2i)q^{5}+5iq^{7}-5q^{11}+iq^{13}+\cdots\)
4680.2.l.d	$4680$	$2$	4680.l	5.b	$2$	$6$	$6$	$37.370$	6.0.350464.1	None					520.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{4})q^{5}+(-\beta _{3}+\beta _{4}+\beta _{5})q^{7}+\cdots\)
4680.2.l.e	$4680$	$2$	4680.l	5.b	$2$	$6$	$6$	$37.370$	6.0.5161984.1	None					1560.2.l.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+(2-\beta _{4}-\beta _{5})q^{11}-\beta _{3}q^{13}+\cdots\)
4680.2.l.f	$4680$	$2$	4680.l	5.b	$2$	$8$	$8$	$37.370$	8.0.1698758656.6	None					1560.2.l.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{2}+\beta _{3})q^{5}-\beta _{4}q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
4680.2.l.g	$4680$	$2$	4680.l	5.b	$2$	$8$	$8$	$37.370$	8.0.\(\cdots\).2	None					1560.2.l.d	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
4680.2.l.h	$4680$	$2$	4680.l	5.b	$2$	$10$	$10$	$37.370$	10.0.\(\cdots\).1	None					1560.2.l.f	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-\beta _{9}q^{7}+(-1+\beta _{4})q^{11}+\cdots\)
4680.2.l.i	$4680$	$2$	4680.l	5.b	$2$	$10$	$10$	$37.370$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					520.2.d.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+\beta _{4}q^{7}+(-3+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
4680.2.l.j	$4680$	$2$	4680.l	5.b	$2$	$18$	$18$	$37.370$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			4680.2.l.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(-1-\beta _{13}+\cdots)q^{11}+\cdots\)
4680.2.l.k	$4680$	$2$	4680.l	5.b	$2$	$18$	$18$	$37.370$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			4680.2.l.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(1+\beta _{13}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4680, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4680, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2340, [\chi])\)\(^{\oplus 2}\)