Space of modular forms of level 1776, weight 2, and Character 1776.q

• Label: 1776.2.q
• Level: $1776$
• Weight: $2$
• Character orbit: 1776.q
• Rep. character: $\chi_{1776}(433,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $76$
• Newform subspaces: $17$
• Sturm bound: $608$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1776 = 2^{4} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1776.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(608\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1776, [\chi])\).

	Total	New	Old
Modular forms	632	76	556
Cusp forms	584	76	508
Eisenstein series	48	0	48

Trace form

76 * q - 2 * q^3 - 2 * q^5 + 6 * q^7 - 38 * q^9 + 8 * q^11 + 4 * q^13 + 2 * q^17 - 4 * q^19 + 8 * q^23 - 36 * q^25 + 4 * q^27 - 12 * q^29 - 4 * q^31 + 18 * q^37 + 2 * q^39 + 18 * q^41 - 20 * q^43 + 4 * q^45 - 18 * q^49 + 12 * q^53 - 8 * q^57 - 2 * q^61 - 12 * q^63 + 4 * q^65 - 2 * q^67 + 20 * q^71 + 32 * q^73 + 28 * q^75 + 8 * q^77 + 10 * q^79 - 38 * q^81 - 24 * q^83 + 12 * q^85 + 2 * q^89 + 10 * q^91 - 8 * q^93 - 12 * q^97 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1776, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1776.2.q.a	$1776$	$2$	1776.q	37.c	$3$	$2$	$1$	$14.181$	\(\Q(\sqrt{-3}) \)	None					888.2.q.c	$2$	$1$	\(0\)	\(-1\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}-4\zeta_{6}q^{5}+\zeta_{6}q^{7}+(-1+\zeta_{6})q^{9}+\cdots\)
1776.2.q.b	$1776$	$2$	1776.q	37.c	$3$	$2$	$1$	$14.181$	\(\Q(\sqrt{-3}) \)	None					444.2.i.a	$2$	$1$	\(0\)	\(-1\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-3\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1776.2.q.c	$1776$	$2$	1776.q	37.c	$3$	$2$	$1$	$14.181$	\(\Q(\sqrt{-3}) \)	None					222.2.e.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}-3\zeta_{6}q^{7}+(-1+\zeta_{6})q^{9}+\cdots\)
1776.2.q.d	$1776$	$2$	1776.q	37.c	$3$	$2$	$1$	$14.181$	\(\Q(\sqrt{-3}) \)	None					888.2.q.d	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}+\zeta_{6}q^{5}-4\zeta_{6}q^{7}+(-1+\zeta_{6})q^{9}+\cdots\)
1776.2.q.e	$1776$	$2$	1776.q	37.c	$3$	$2$	$1$	$14.181$	\(\Q(\sqrt{-3}) \)	None					222.2.e.b	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{7}+(-1+\zeta_{6})q^{9}+\cdots\)
1776.2.q.f	$1776$	$2$	1776.q	37.c	$3$	$2$	$1$	$14.181$	\(\Q(\sqrt{-3}) \)	None					888.2.q.b	$2$	$0$	\(0\)	\(1\)	\(2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{3}+2\zeta_{6}q^{5}+3\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1776.2.q.g	$1776$	$2$	1776.q	37.c	$3$	$2$	$1$	$14.181$	\(\Q(\sqrt{-3}) \)	None					888.2.q.a	$2$	$0$	\(0\)	\(1\)	\(2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{3}+2\zeta_{6}q^{5}+3\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1776.2.q.h	$1776$	$2$	1776.q	37.c	$3$	$4$	$2$	$14.181$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					222.2.e.c	$2$	$0$	\(0\)	\(-2\)	\(-1\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}-\beta _{3})q^{7}+\cdots\)
1776.2.q.i	$1776$	$2$	1776.q	37.c	$3$	$4$	$2$	$14.181$	\(\Q(\sqrt{-3}, \sqrt{37})\)	None					444.2.i.b	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+\beta _{1}q^{5}+3\beta _{2}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
1776.2.q.j	$1776$	$2$	1776.q	37.c	$3$	$6$	$3$	$14.181$	6.0.1415907.1	None					888.2.q.f	$2$	$0$	\(0\)	\(-3\)	\(-2\)	\(7\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{3}+(\beta _{1}-\beta _{3}-\beta _{4})q^{5}+(\beta _{1}+2\beta _{3}+\cdots)q^{7}+\cdots\)
1776.2.q.k	$1776$	$2$	1776.q	37.c	$3$	$6$	$3$	$14.181$	6.0.47545083.2	None					888.2.q.g	$2$	$0$	\(0\)	\(-3\)	\(1\)	\(-9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}-\beta _{5}q^{5}+3\beta _{4}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
1776.2.q.l	$1776$	$2$	1776.q	37.c	$3$	$6$	$3$	$14.181$	6.0.1415907.1	None					111.2.e.a	$2$	$0$	\(0\)	\(-3\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}+(-\beta _{4}-\beta _{5})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1776.2.q.m	$1776$	$2$	1776.q	37.c	$3$	$6$	$3$	$14.181$	6.0.50898483.1	None					888.2.q.h	$2$	$0$	\(0\)	\(-3\)	\(3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\beta _{3}q^{7}+\cdots\)
1776.2.q.n	$1776$	$2$	1776.q	37.c	$3$	$6$	$3$	$14.181$	6.0.1415907.1	None					888.2.q.e	$2$	$0$	\(0\)	\(3\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{4})q^{3}+(-2+\beta _{1}-2\beta _{4})q^{5}+\cdots\)
1776.2.q.o	$1776$	$2$	1776.q	37.c	$3$	$6$	$3$	$14.181$	6.0.27379323.1	None					444.2.i.c	$2$	$0$	\(0\)	\(3\)	\(-1\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}-\beta _{1}q^{5}+\beta _{4}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
1776.2.q.p	$1776$	$2$	1776.q	37.c	$3$	$8$	$4$	$14.181$	8.0.1445900625.1	None					888.2.q.i	$2$	$0$	\(0\)	\(4\)	\(1\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{3})q^{3}+(-\beta _{4}+\beta _{5}-\beta _{6})q^{5}+\cdots\)
1776.2.q.q	$1776$	$2$	1776.q	37.c	$3$	$10$	$5$	$14.181$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None			✓		111.2.e.b	$2$	$0$	\(0\)	\(5\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{6})q^{3}-\beta _{9}q^{5}+(\beta _{3}+\beta _{7})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1776, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1776, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(888, [\chi])\)\(^{\oplus 2}\)