Space of modular forms of level 1520, weight 2, and Character 1520.bq

• Label: 1520.2.bq
• Level: $1520$
• Weight: $2$
• Character orbit: 1520.bq
• Rep. character: $\chi_{1520}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $18$
• Sturm bound: $480$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.bq (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(480\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1520, [\chi])\).

	Total	New	Old
Modular forms	504	80	424
Cusp forms	456	80	376
Eisenstein series	48	0	48

Trace form

\( 80 q - 28 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1520, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1520.2.bq.a	$1520$	$2$	1520.bq	76.f	$6$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1520.2.bq.b	$1520$	$2$	1520.bq	76.f	$6$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1520.2.bq.c	$1520$	$2$	1520.bq	76.f	$6$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1520.2.bq.d	$1520$	$2$	1520.bq	76.f	$6$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1520.2.bq.e	$1520$	$2$	1520.bq	76.f	$6$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
1520.2.bq.f	$1520$	$2$	1520.bq	76.f	$6$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
1520.2.bq.g	$1520$	$2$	1520.bq	76.f	$6$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1520.2.bq.h	$1520$	$2$	1520.bq	76.f	$6$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+(1-2\zeta_{6})q^{7}+\cdots\)
1520.2.bq.i	$1520$	$2$	1520.bq	76.f	$6$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1520.2.bq.j	$1520$	$2$	1520.bq	76.f	$6$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1520.2.bq.k	$1520$	$2$	1520.bq	76.f	$6$	$4$	$2$	$12.137$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(-4\)	\(2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
1520.2.bq.l	$1520$	$2$	1520.bq	76.f	$6$	$4$	$2$	$12.137$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(4\)	\(2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-2\beta _{1}q^{3}-\beta _{1}q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
1520.2.bq.m	$1520$	$2$	1520.bq	76.f	$6$	$6$	$3$	$12.137$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(-3\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{18}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\zeta_{18}^{3}q^{5}+\cdots\)
1520.2.bq.n	$1520$	$2$	1520.bq	76.f	$6$	$6$	$3$	$12.137$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(3\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(1+\cdots)q^{5}+\cdots\)
1520.2.bq.o	$1520$	$2$	1520.bq	76.f	$6$	$8$	$4$	$12.137$	8.0.1121513121.1	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{5})q^{3}+(-1+\beta _{6})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
1520.2.bq.p	$1520$	$2$	1520.bq	76.f	$6$	$8$	$4$	$12.137$	8.0.1121513121.1	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}-\beta _{5})q^{3}+(-1+\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1520.2.bq.q	$1520$	$2$	1520.bq	76.f	$6$	$12$	$6$	$12.137$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{3}+(-1+\beta _{6})q^{5}+(-2\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
1520.2.bq.r	$1520$	$2$	1520.bq	76.f	$6$	$12$	$6$	$12.137$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}+\beta _{5})q^{3}-\beta _{4}q^{5}-\beta _{9}q^{7}+(-2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \cong \)