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

• 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: $7$

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

80 * q - 4 * q^3 - 8 * q^7 - 44 * q^9 + 4 * q^15 + 8 * q^17 + 12 * q^19 - 40 * q^25 + 32 * q^27 - 24 * q^31 - 12 * q^33 - 8 * q^39 + 16 * q^43 + 72 * q^49 - 4 * q^51 - 8 * q^53 - 8 * q^57 - 24 * q^61 + 16 * q^63 - 16 * q^65 - 8 * q^67 + 32 * q^69 + 12 * q^71 - 4 * q^73 + 8 * q^75 + 16 * q^77 + 12 * q^79 - 48 * q^81 + 48 * q^83 + 8 * q^85 - 4 * q^89 + 8 * q^91 - 36 * q^97 + 16 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1520.2.q.a	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None					760.2.q.b	$2$	$1$	\(0\)	\(-2\)	\(-1\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-4q^{7}+\cdots\)
1520.2.q.b	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None					760.2.q.c	$2$	$1$	\(0\)	\(-2\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1520.2.q.c	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None					95.2.e.a	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+4q^{7}+\cdots\)
1520.2.q.d	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None					760.2.q.a	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+2q^{7}+\cdots\)
1520.2.q.e	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None					190.2.e.b	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-2q^{7}+\cdots\)
1520.2.q.f	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None					190.2.e.a	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}-5q^{11}+\cdots\)
1520.2.q.g	$1520$	$2$	1520.q	19.c	$3$	$2$	$1$	$12.137$	\(\Q(\sqrt{-3}) \)	None					380.2.i.a	$2$	$0$	\(0\)	\(2\)	\(1\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+4q^{7}+\cdots\)
1520.2.q.h	$1520$	$2$	1520.q	19.c	$3$	$4$	$2$	$12.137$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None					190.2.e.c	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-3-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1520.2.q.i	$1520$	$2$	1520.q	19.c	$3$	$6$	$3$	$12.137$	6.0.1783323.2	None					380.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{5})q^{3}+(1+\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1520.2.q.j	$1520$	$2$	1520.q	19.c	$3$	$6$	$3$	$12.137$	6.0.3518667.1	None					95.2.e.b	$2$	$0$	\(0\)	\(1\)	\(3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+(-2+\cdots)q^{9}+\cdots\)
1520.2.q.k	$1520$	$2$	1520.q	19.c	$3$	$8$	$4$	$12.137$	8.0.4601315889.1	None					760.2.q.f	$2$	$0$	\(0\)	\(-1\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{7}q^{3}-\beta _{5}q^{5}+(\beta _{2}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots\)
1520.2.q.l	$1520$	$2$	1520.q	19.c	$3$	$8$	$4$	$12.137$	8.0.\(\cdots\).1	None					760.2.q.e	$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{4})q^{3}+\beta _{5}q^{5}+(1+\beta _{4}-2\beta _{7})q^{7}+\cdots\)
1520.2.q.m	$1520$	$2$	1520.q	19.c	$3$	$8$	$4$	$12.137$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					380.2.i.c	$2$	$0$	\(0\)	\(1\)	\(-4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1520.2.q.n	$1520$	$2$	1520.q	19.c	$3$	$8$	$4$	$12.137$	8.0.\(\cdots\).1	None					760.2.q.d	$2$	$0$	\(0\)	\(1\)	\(-4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(1-\beta _{3})q^{7}+(-4+\cdots)q^{9}+\cdots\)
1520.2.q.o	$1520$	$2$	1520.q	19.c	$3$	$8$	$4$	$12.137$	8.0.4601315889.1	None					95.2.e.c	$2$	$0$	\(0\)	\(3\)	\(-4\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{5}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
1520.2.q.p	$1520$	$2$	1520.q	19.c	$3$	$10$	$5$	$12.137$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None			✓		760.2.q.g	$2$	$0$	\(0\)	\(-1\)	\(5\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+(1-\beta _{6})q^{5}+(-1-\beta _{5})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)