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

• Label: 2520.2.bi
• Level: $2520$
• Weight: $2$
• Character orbit: 2520.bi
• Rep. character: $\chi_{2520}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $19$
• Sturm bound: $1152$
• Trace bound: $13$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	1216	80	1136
Cusp forms	1088	80	1008
Eisenstein series	128	0	128

Trace form

\( 80 q + 2 q^{5} - 4 q^{7} + O(q^{10}) \)

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.bi.a	$2520$	$2$	2520.bi	7.c	$3$	$2$	$1$	$20.122$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2520.2.bi.b	$2520$	$2$	2520.bi	7.c	$3$	$2$	$1$	$20.122$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
2520.2.bi.c	$2520$	$2$	2520.bi	7.c	$3$	$2$	$1$	$20.122$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(2-3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2520.2.bi.d	$2520$	$2$	2520.bi	7.c	$3$	$2$	$1$	$20.122$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2520.2.bi.e	$2520$	$2$	2520.bi	7.c	$3$	$2$	$1$	$20.122$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
2520.2.bi.f	$2520$	$2$	2520.bi	7.c	$3$	$2$	$1$	$20.122$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2520.2.bi.g	$2520$	$2$	2520.bi	7.c	$3$	$2$	$1$	$20.122$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}-q^{13}+(2+\cdots)q^{17}+\cdots\)
2520.2.bi.h	$2520$	$2$	2520.bi	7.c	$3$	$2$	$1$	$20.122$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
2520.2.bi.i	$2520$	$2$	2520.bi	7.c	$3$	$2$	$1$	$20.122$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
2520.2.bi.j	$2520$	$2$	2520.bi	7.c	$3$	$4$	$2$	$20.122$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
2520.2.bi.k	$2520$	$2$	2520.bi	7.c	$3$	$4$	$2$	$20.122$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{5}+(-1-\beta _{1}-\beta _{2}-2\beta _{3})q^{7}+\cdots\)
2520.2.bi.l	$2520$	$2$	2520.bi	7.c	$3$	$4$	$2$	$20.122$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{5}+(\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\beta _{1}q^{11}+\cdots\)
2520.2.bi.m	$2520$	$2$	2520.bi	7.c	$3$	$6$	$3$	$20.122$	6.0.4406832.1	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{4})q^{5}+(-\beta _{2}-\beta _{5})q^{7}+(\beta _{4}+\cdots)q^{11}+\cdots\)
2520.2.bi.n	$2520$	$2$	2520.bi	7.c	$3$	$6$	$3$	$20.122$	6.0.29428272.1	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{3})q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
2520.2.bi.o	$2520$	$2$	2520.bi	7.c	$3$	$6$	$3$	$20.122$	6.0.38363328.2	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{5}+(-\beta _{1}+\beta _{4})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2520.2.bi.p	$2520$	$2$	2520.bi	7.c	$3$	$6$	$3$	$20.122$	6.0.4406832.1	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4})q^{5}+(-\beta _{2}-\beta _{5})q^{7}+(-\beta _{4}+\cdots)q^{11}+\cdots\)
2520.2.bi.q	$2520$	$2$	2520.bi	7.c	$3$	$6$	$3$	$20.122$	6.0.11337408.1	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{5}+(1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{7}+\cdots\)
2520.2.bi.r	$2520$	$2$	2520.bi	7.c	$3$	$10$	$5$	$20.122$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-5\)	\(-1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{5}+\beta _{6}q^{7}+\beta _{3}q^{11}+(\beta _{4}-\beta _{6}+\cdots)q^{13}+\cdots\)
2520.2.bi.s	$2520$	$2$	2520.bi	7.c	$3$	$10$	$5$	$20.122$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(5\)	\(-1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{5}+\beta _{6}q^{7}-\beta _{3}q^{11}+(\beta _{4}-\beta _{6}+\cdots)q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)