Space of modular forms of level 1782, weight 2, and Character 1782.e

• Label: 1782.2.e
• Level: $1782$
• Weight: $2$
• Character orbit: 1782.e
• Rep. character: $\chi_{1782}(595,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $30$
• Sturm bound: $648$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1782 = 2 \cdot 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1782.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 30 \)
Sturm bound:			\(648\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1782, [\chi])\).

	Total	New	Old
Modular forms	696	80	616
Cusp forms	600	80	520
Eisenstein series	96	0	96

Trace form

\( 80 q - 40 q^{4} - 20 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1782, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1782.2.e.a	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
1782.2.e.b	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
1782.2.e.c	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
1782.2.e.d	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
1782.2.e.e	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
1782.2.e.f	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)
1782.2.e.g	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)
1782.2.e.h	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)
1782.2.e.i	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(0\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
1782.2.e.j	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1782.2.e.k	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(0\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}+\cdots\)
1782.2.e.l	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}+\cdots\)
1782.2.e.m	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(1\)	\(0\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1782.2.e.n	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1782.2.e.o	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
1782.2.e.p	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
1782.2.e.q	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)
1782.2.e.r	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)
1782.2.e.s	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)
1782.2.e.t	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1782.2.e.u	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1782.2.e.v	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
1782.2.e.w	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1782.2.e.x	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
1782.2.e.y	$1782$	$2$	1782.e	9.c	$3$	$4$	$2$	$14.229$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1782.2.e.z	$1782$	$2$	1782.e	9.c	$3$	$4$	$2$	$14.229$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{12}q^{2}+(-1+\zeta_{12})q^{4}+(1-\zeta_{12}+\cdots)q^{5}+\cdots\)
1782.2.e.ba	$1782$	$2$	1782.e	9.c	$3$	$4$	$2$	$14.229$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{12}q^{2}+(-1+\zeta_{12})q^{4}+(-1+\zeta_{12}+\cdots)q^{5}+\cdots\)
1782.2.e.bb	$1782$	$2$	1782.e	9.c	$3$	$4$	$2$	$14.229$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		$2$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1782.2.e.bc	$1782$	$2$	1782.e	9.c	$3$	$8$	$4$	$14.229$	8.0.3887771904.9	None		$2$	$0$	\(-4\)	\(0\)	\(2\)	\(-6\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(1+\beta _{5}-\beta _{7})q^{5}+\cdots\)
1782.2.e.bd	$1782$	$2$	1782.e	9.c	$3$	$8$	$4$	$14.229$	8.0.3887771904.9	None		$2$	$0$	\(4\)	\(0\)	\(-2\)	\(-6\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+\beta _{5}q^{5}+(-1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1782, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1782, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(594, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(891, [\chi])\)\(^{\oplus 2}\)