Space of modular forms of level 2520, weight 2, and Character 2520.t

• Label: 2520.2.t
• Level: $2520$
• Weight: $2$
• Character orbit: 2520.t
• Rep. character: $\chi_{2520}(1009,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $11$
• Sturm bound: $1152$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.t (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(1152\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2520, [\chi])\).

	Total	New	Old
Modular forms	608	44	564
Cusp forms	544	44	500
Eisenstein series	64	0	64

Trace form

\( 44 q + 4 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2520, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2520.2.t.a	$2520$	$2$	2520.t	5.b	$2$	$2$	$2$	$20.122$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+i)q^{5}+iq^{7}+q^{11}-iq^{13}+\cdots\)
2520.2.t.b	$2520$	$2$	2520.t	5.b	$2$	$2$	$2$	$20.122$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+2i)q^{5}+iq^{7}+2q^{11}+2iq^{13}+\cdots\)
2520.2.t.c	$2520$	$2$	2520.t	5.b	$2$	$2$	$2$	$20.122$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2i)q^{5}+iq^{7}-2q^{11}+2iq^{13}+\cdots\)
2520.2.t.d	$2520$	$2$	2520.t	5.b	$2$	$2$	$2$	$20.122$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2i)q^{5}+iq^{7}-2q^{11}+2iq^{13}+\cdots\)
2520.2.t.e	$2520$	$2$	2520.t	5.b	$2$	$2$	$2$	$20.122$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2i)q^{5}-iq^{7}-2q^{11}-2iq^{13}+\cdots\)
2520.2.t.f	$2520$	$2$	2520.t	5.b	$2$	$4$	$4$	$20.122$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+\beta _{1}q^{7}+2q^{11}-2\beta _{2}q^{13}+\cdots\)
2520.2.t.g	$2520$	$2$	2520.t	5.b	$2$	$6$	$6$	$20.122$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{5})q^{5}+\beta _{4}q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
2520.2.t.h	$2520$	$2$	2520.t	5.b	$2$	$6$	$6$	$20.122$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}-\beta _{1}q^{7}+(-2+\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
2520.2.t.i	$2520$	$2$	2520.t	5.b	$2$	$6$	$6$	$20.122$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+\beta _{1}q^{7}+(2-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
2520.2.t.j	$2520$	$2$	2520.t	5.b	$2$	$6$	$6$	$20.122$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}+\beta _{1}q^{7}+(-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
2520.2.t.k	$2520$	$2$	2520.t	5.b	$2$	$6$	$6$	$20.122$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}-\beta _{1}q^{7}+(\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1260, [\chi])\)\(^{\oplus 2}\)