⌂ → Modular forms → Classical → Level 1520 → Weight 2 → Character orbit q

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

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Properties

Label	1520.2.q

Level	$1520$
Weight	$2$
Character orbit	1520.q
Rep. character	$\chi_{1520}(881,\cdot)$
Character field	$\Q(\zeta_{3})$
Dimension	$80$
Newform subspaces	$16$
Sturm bound	$480$
Trace bound	$7$

Related objects

Newspace 1520.2

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Defining parameters

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(480\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

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

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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
1520.2.q.a	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(-1\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-4q^{7}+\cdots\)
1520.2.q.b	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1520.2.q.c	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(1\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+4q^{7}+\cdots\)
1520.2.q.d	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+2q^{7}+\cdots\)
1520.2.q.e	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-2q^{7}+\cdots\)
1520.2.q.f	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}-5q^{11}+\cdots\)
1520.2.q.g	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(1\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+4q^{7}+\cdots\)
1520.2.q.h	$1520$	$2$	1520.q	19.c	$3$	$4$	$2$	$12.137$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-3-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1520.2.q.i	$1520$	$2$	1520.q	19.c	$3$	$6$	$3$	$12.137$	6.0.1783323.2	None		$2$	$0$	\(0\)	\(-1\)	\(3\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{5})q^{3}+(1+\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1520.2.q.j	$1520$	$2$	1520.q	19.c	$3$	$6$	$3$	$12.137$	6.0.3518667.1	None		$2$	$0$	\(0\)	\(1\)	\(3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+(-2+\cdots)q^{9}+\cdots\)
1520.2.q.k	$1520$	$2$	1520.q	19.c	$3$	$8$	$4$	$12.137$	8.0.4601315889.1	None		$2$	$0$	\(0\)	\(-1\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{7}q^{3}-\beta _{5}q^{5}+(\beta _{2}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots\)
1520.2.q.l	$1520$	$2$	1520.q	19.c	$3$	$8$	$4$	$12.137$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{4})q^{3}+\beta _{5}q^{5}+(1+\beta _{4}-2\beta _{7})q^{7}+\cdots\)
1520.2.q.m	$1520$	$2$	1520.q	19.c	$3$	$8$	$4$	$12.137$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(1\)	\(-4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1520.2.q.n	$1520$	$2$	1520.q	19.c	$3$	$8$	$4$	$12.137$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(1\)	\(-4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(1-\beta _{3})q^{7}+(-4+\cdots)q^{9}+\cdots\)
1520.2.q.o	$1520$	$2$	1520.q	19.c	$3$	$8$	$4$	$12.137$	8.0.4601315889.1	None		$2$	$0$	\(0\)	\(3\)	\(-4\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{5}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
1520.2.q.p	$1520$	$2$	1520.q	19.c	$3$	$10$	$5$	$12.137$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(-1\)	\(5\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+(1-\beta _{6})q^{5}+(-1-\beta _{5})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)